我从杰克逊·成加莱先生的暗示中得到了解决方案。

创建一个Okhttp请求拦截器

private static class PicassoInterceptor implements Interceptor {

    @Override
    public Response intercept(Chain chain) throws IOException {

        final MediaType JSON
                = MediaType.parse("application/json; charset=utf-8");
        Map<String, String> map = new HashMap<String, String>();
        map.put("session_id", session_id);
        map.put("image", image);
        String requestJsonBody = new Gson().toJson(map);
        RequestBody body = RequestBody.create(JSON, requestStringBody);
        final Request original = chain.request();
        final Request.Builder requestBuilder = original.newBuilder()
                .url(url)
                .post(body);
        return chain.proceed(requestBuilder.build());
    }
}

创建一个Okhttp客户端，添加此拦截器

OkHttpClient okHttpClient = new OkHttpClient();
okHttpClient.interceptors().add(new PicassoInterceptor());

使用此okhttp客户端创建Dowloader

OkHttpDownloader = downloader = new OkHttpDownloader(okHttpClient)

使用此下载器构建毕加索

Picasso picasso = new Picasso.Builder(context).downloader(downloader ).build();