Java Code:
import org.eclipse.swt.SWT;
import org.eclipse.swt.custom.LineBackgroundEvent;
import org.eclipse.swt.custom.LineBackgroundListener;
import org.eclipse.swt.custom.StyledText;
import org.eclipse.swt.layout.GridData;
import org.eclipse.swt.layout.GridLayout;
import org.eclipse.swt.widgets.Display;
import org.eclipse.swt.widgets.Shell;

public class HighlightOddLine {
  Display display = new Display();
  Shell shell = new Shell(display);
  StyledText styledText;
  public HighlightOddLine() {
    shell.setLayout(new GridLayout());
    styledText = new StyledText(shell, SWT.MULTI | SWT.WRAP | SWT.BORDER | SWT.H_SCROLL | SWT.V_SCROLL);
    styledText.setLayoutData(new GridData(GridData.FILL_BOTH));
    styledText.addLineBackgroundListener(new LineBackgroundListener() {
      public void lineGetBackground(LineBackgroundEvent event) {
        if(styledText.getLineAtOffset(event.lineOffset) % 2 == 1)
          event.lineBackground = shell.getDisplay().getSystemColor(SWT.COLOR_YELLOW);
      }
    });
    styledText.setText("Line 0\r\nLine 1\r\nLine 2\r\nLine 3\r\nLine 4\r\nLine 5\r\nLine 6");

    shell.setSize(300, 150);
    shell.open();
    //textUser.forceFocus();

    // Set up the event loop.
    while (!shell.isDisposed()) {
      if (!display.readAndDispatch()) {
        // If no more entries in event queue
        display.sleep();
      }
    }

    display.dispose();
  }

  private void init() {

  }

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