ActivityManager manager = (ActivityManager) mContext.getSystemService(Context.ACTIVITY_SERVICE);
for (RunningServiceInfo service : manager.getRunningServices(Integer.MAX_VALUE)) {
    if (serviceName.equals(service.service.getClassName())) {
        return true;
    }
}

PS：

serviceName 服务名称（完整的服务名称，包括包名，如com.xxx.xxxService）

/**
 * 5.0以上版本
 * 需要使用系统签名,同时需要<uses-permission android:name="android.permission.DUMP"/>或声明系统用户
 *
 */
public static ComponentName getTopActivity_L_U() {
    String cmd = "dumpsys activity activities | grep mResumedActivity";//"dumpsys activity";
    String pkgName = "";
    String className = "";
    String s = "";
    ComponentName result = null;
    Process p = null;
    try {
        p = Runtime.getRuntime().exec(cmd);
        BufferedReader in = new BufferedReader(new InputStreamReader(p.getInputStream()));
        String line = null;
        while ((line = in.readLine()) != null) {
            if (line.contains("mResumedActivity")) {
                s = line;
                break;
            }
        }
        if (CommonUtil.isNotEmpty(s)) {
            String info = s.substring(s.indexOf("u0 ") + 3, s.lastIndexOf(" "));
            pkgName = info.split("/")[0];

            className = info.split("/")[1];
            if (className.startsWith(".")) {
                className = pkgName + className;
            }

            if (CommonUtil.isNotEmpty(pkgName) && CommonUtil.isNotEmpty(className)) {
                result = new ComponentName(pkgName, className);
            }
        }

    } catch (IOException e) {
        // TODO Auto-generated catch block
        e.printStackTrace();
    } finally {
        try {
            p.getInputStream().close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
    return result;

}

/**
 * 5.0以下版本
 *
 * @param context
 * @return
 */
public static ComponentName getTopActivity_L_D(Context context) {
    ActivityManager am = (ActivityManager) context
            .getSystemService(context.ACTIVITY_SERVICE);
    ComponentName cn = am.getRunningTasks(1).get(0).topActivity;
    return cn;
}