diff --git a/cmd/gpu_plugin/gpu_plugin.go b/cmd/gpu_plugin/gpu_plugin.go
index d820974b..23a497a9 100644
--- a/cmd/gpu_plugin/gpu_plugin.go
+++ b/cmd/gpu_plugin/gpu_plugin.go
@@ -64,15 +64,58 @@ type cliOptions struct {
 
 type preferredAllocationPolicyFunc func(*pluginapi.ContainerPreferredAllocationRequest) []string
 
-// nonePolicy is used for allocating GPU devices randomly.
+// nonePolicy is used for allocating GPU devices randomly, while trying
+// to select as many individual GPU devices as requested.
 func nonePolicy(req *pluginapi.ContainerPreferredAllocationRequest) []string {
 	klog.V(2).Info("Select nonePolicy for GPU device allocation")
 
-	deviceIds := req.AvailableDeviceIDs[0:req.AllocationSize]
+	devices := make(map[string]bool)
+	selected := make(map[string]bool)
+	neededCount := req.AllocationSize
 
-	klog.V(2).Infof("Allocate deviceIds: %q", deviceIds)
+	// When shared-dev-num is greater than 1, try to find as
+	// many independent GPUs as possible, to satisfy the request.
 
-	return deviceIds
+	for _, deviceID := range req.AvailableDeviceIDs {
+		device := strings.Split(deviceID, "-")[0]
+
+		if _, found := devices[device]; !found {
+			devices[device] = true
+			selected[deviceID] = true
+			neededCount--
+
+			if neededCount == 0 {
+				break
+			}
+		}
+	}
+
+	// If there were not enough independent GPUs, use remaining untaken deviceIDs.
+
+	if neededCount > 0 {
+		for _, deviceID := range req.AvailableDeviceIDs {
+			if _, found := selected[deviceID]; !found {
+				selected[deviceID] = true
+				neededCount--
+
+				if neededCount == 0 {
+					break
+				}
+			}
+		}
+	}
+
+	// Convert selected map into an array
+
+	deviceIDs := []string{}
+
+	for deviceID := range selected {
+		deviceIDs = append(deviceIDs, deviceID)
+	}
+
+	klog.V(2).Infof("Allocate deviceIds: %q", deviceIDs)
+
+	return deviceIDs
 }
 
 // balancedPolicy is used for allocating GPU devices in balance.
diff --git a/cmd/gpu_plugin/gpu_plugin_test.go b/cmd/gpu_plugin/gpu_plugin_test.go
index 62536093..a5b59519 100644
--- a/cmd/gpu_plugin/gpu_plugin_test.go
+++ b/cmd/gpu_plugin/gpu_plugin_test.go
@@ -20,6 +20,7 @@ import (
 	"path"
 	"path/filepath"
 	"reflect"
+	"sort"
 	"testing"
 
 	"github.com/pkg/errors"
@@ -99,12 +100,21 @@ func TestGetPreferredAllocation(t *testing.T) {
 	rqt := &v1beta1.PreferredAllocationRequest{
 		ContainerRequests: []*v1beta1.ContainerPreferredAllocationRequest{
 			{
-				AvailableDeviceIDs: []string{"card0-4", "card1-1", "card2-3", "card2-4", "card2-1", "card1-0", "card1-4", "card3-4", "card1-2", "card0-1", "card2-0", "card2-2", "card1-3", "card0-2", "card3-0", "card3-3", "card0-3", "card0-0", "card3-1", "card3-2"},
+				AvailableDeviceIDs: []string{"card0-4", "card0-2", "card1-1", "card2-3", "card2-4", "card2-1", "card1-0", "card1-4", "card3-4", "card1-2", "card0-1", "card2-0", "card2-2", "card1-3", "card3-0", "card3-3", "card0-3", "card0-0", "card3-1", "card3-2"},
 				AllocationSize:     4,
 			},
 		},
 	}
 
+	rqtNotEnough := &v1beta1.PreferredAllocationRequest{
+		ContainerRequests: []*v1beta1.ContainerPreferredAllocationRequest{
+			{
+				AvailableDeviceIDs: []string{"card0-1", "card0-2", "card0-3", "card1-1"},
+				AllocationSize:     3,
+			},
+		},
+	}
+
 	rqtErr := &v1beta1.PreferredAllocationRequest{
 		ContainerRequests: []*v1beta1.ContainerPreferredAllocationRequest{
 			{
@@ -117,22 +127,24 @@ func TestGetPreferredAllocation(t *testing.T) {
 	plugin := newDevicePlugin("", "", cliOptions{sharedDevNum: 5, resourceManagement: false, preferredAllocationPolicy: "none"})
 	response, _ := plugin.GetPreferredAllocation(rqt)
 
-	if !reflect.DeepEqual(response.ContainerResponses[0].DeviceIDs, []string{"card0-4", "card1-1", "card2-3", "card2-4"}) {
-		t.Error("Unexpected return value for none preferred allocation")
+	sort.Strings(response.ContainerResponses[0].DeviceIDs)
+
+	if !reflect.DeepEqual(response.ContainerResponses[0].DeviceIDs, []string{"card0-4", "card1-1", "card2-3", "card3-4"}) {
+		t.Error("Unexpected return value for none preferred allocation", response.ContainerResponses[0].DeviceIDs)
 	}
 
 	plugin = newDevicePlugin("", "", cliOptions{sharedDevNum: 5, resourceManagement: false, preferredAllocationPolicy: "balanced"})
 	response, _ = plugin.GetPreferredAllocation(rqt)
 
 	if !reflect.DeepEqual(response.ContainerResponses[0].DeviceIDs, []string{"card0-0", "card1-0", "card2-0", "card3-0"}) {
-		t.Error("Unexpected return value for balanced preferred allocation")
+		t.Error("Unexpected return value for balanced preferred allocation", response.ContainerResponses[0].DeviceIDs)
 	}
 
 	plugin = newDevicePlugin("", "", cliOptions{sharedDevNum: 5, resourceManagement: false, preferredAllocationPolicy: "packed"})
 	response, _ = plugin.GetPreferredAllocation(rqt)
 
 	if !reflect.DeepEqual(response.ContainerResponses[0].DeviceIDs, []string{"card0-0", "card0-1", "card0-2", "card0-3"}) {
-		t.Error("Unexpected return value for packed preferred allocation")
+		t.Error("Unexpected return value for packed preferred allocation", response.ContainerResponses[0].DeviceIDs)
 	}
 
 	plugin = newDevicePlugin("", "", cliOptions{sharedDevNum: 5, resourceManagement: false, preferredAllocationPolicy: "none"})
@@ -141,6 +153,16 @@ func TestGetPreferredAllocation(t *testing.T) {
 	if response != nil {
 		t.Error("Fail to handle the input error that req.AllocationSize is greater than len(req.AvailableDeviceIDs).")
 	}
+
+	plugin = newDevicePlugin("", "", cliOptions{sharedDevNum: 5, resourceManagement: false, preferredAllocationPolicy: "none"})
+	response, _ = plugin.GetPreferredAllocation(rqtNotEnough)
+
+	sort.Strings(response.ContainerResponses[0].DeviceIDs)
+
+	if !reflect.DeepEqual(response.ContainerResponses[0].DeviceIDs, []string{"card0-1", "card0-2", "card1-1"}) {
+		t.Error("Unexpected return value for none preferred allocation with too few separate devices",
+			response.ContainerResponses[0].DeviceIDs)
+	}
 }
 
 func TestAllocate(t *testing.T) {