1、使用AsyncTask异步任务实现，调用publishProgress()方法刷新进度来实现（已优化）

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public class MyAsyncTask extends AsyncTask {
  private Context context;
  private NotificationManager notificationManager;
  private NotificationCompat.Builder builder;
  public MyAsyncTask(Context context){
    this.context = context;
    notificationManager = (NotificationManager) context.getSystemService(Activity.NOTIFICATION_SERVICE);
    builder = new NotificationCompat.Builder(context);
  }
  @Override
  protected void onPreExecute() {
    super.onPreExecute();
    builder.setSmallIcon(R.mipmap.ic_launcher)
        .setContentInfo("下载中...")
        .setContentTitle("正在下载");
  }
  @Override
  protected Integer doInBackground(String... params) {
    Log.e(TAG, "doInBackground: "+params[0] );
    InputStream is = null;
    OutputStream os = null;
    HttpURLConnection connection = null;
    int total_length = 0;
    try {
      URL url1 = new URL(params[0]);
      connection = (HttpURLConnection) url1.openConnection();
      connection.setRequestMethod("GET");
      connection.setReadTimeout(50000);
      connection.connect();
      if(connection.getResponseCode() == 200){
        is = connection.getInputStream();
        os = new FileOutputStream("/sdcard/zongzhi.apk");
        byte [] buf = new byte[1024];
        int len;
        int pro1=0;
        int pro2=0;
        // 获取文件流大小，用于更新进度
        long file_length = connection.getContentLength();
        while((len = is.read(buf))!=-1){
          total_length += len;
          if(file_length>0) {
            pro1 = (int) ((total_length / (float) file_length) * 100);//传递进度（注意顺序）
          }
          if(pro1!=pro2) {
            // 调用update函数，更新进度
            publishProgress(pro2=pro1);
          }
          os.write(buf, 0, len);
        }
      }
    } catch (MalformedURLException e) {
      e.printStackTrace();
    } catch (IOException e) {
      e.printStackTrace();
    }finally {
      try {
        if (is != null) {
          is.close();
        }
        if (os != null) {
          os.close();
        }
      } catch (IOException e) {
        e.printStackTrace();
      }
      if (connection != null) {
        connection.disconnect();
      }
    }
    return total_length;
  }
  @Override
  protected void onCancelled(Integer integer) {
    super.onCancelled(integer);
  }
  @Override
  protected void onCancelled() {
    super.onCancelled();
  }
  @Override
  protected void onProgressUpdate(Integer... values) {
    super.onProgressUpdate(values);
    builder.setProgress(100,values[0],false);
    notificationManager.notify(0x3,builder.build());
    //下载进度提示
    builder.setContentText("下载"+values[0]+"%");
    if(values[0]==100) {  //下载完成后点击安装
      Intent it = new Intent(Intent.ACTION_VIEW);
      it.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
      it.setDataAndType(Uri.parse("file:///sdcard/zongzhi.apk"), "application/vnd.android.package-archive");
      PendingIntent pendingIntent = PendingIntent.getActivity(context, 0, it, PendingIntent.FLAG_UPDATE_CURRENT);
      builder.setContentTitle("下载完成")
          .setContentText("点击安装")
          .setContentInfo("下载完成")
          .setContentIntent(pendingIntent);
      notificationManager.notify(0x3, builder.build());
    }
  }
  @Override
  protected void onPostExecute(Integer integer) {
    super.onPostExecute(integer);
    if(integer == 100) {
      Toast.makeText(context, "下载完成", Toast.LENGTH_SHORT).show();
    }
  }
}

文章题目：Android下载文件通知栏显示进度条功能的实例代码-创新互联
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