To reproduce run following code




import javafx.application.Application;
import javafx.scene.Parent;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.control.Hyperlink;
import javafx.scene.layout.VBox;
import javafx.scene.paint.Color;
import javafx.scene.shape.Rectangle;
import javafx.stage.Stage;

public class HyperlinkBackground extends Application {

    public static void main(String[] args) {
        launch( args);
    }

    private Parent getContent() {
        VBox list = new VBox(10);
        
        Hyperlink link = new Hyperlink("Hyperlink\n\n long\n\n long line");
        link.setGraphic(new Rectangle(30,30, Color.BLUE));
        link.setStyle("-fx-background-color: "
                    + "green;"
                    + "-fx-background-insets: 10;"+"-fx-border-color: black;");
        link.setPrefSize(200, 200);
        link.setFocusTraversable(false);
        list.getChildren().add(link);
        return list;
    }

    public void start(Stage stage) {
        stage.setX(100);
        stage.setY(100);
        stage.setWidth(300);
        stage.setHeight(300);
        Scene scene = new Scene(getContent());
        stage.setScene(scene);
        stage.setVisible(true);
    }
}