我用的okhttp，所以直接用的同一个client,在网上找的直接用OkhttpDownload不行，看原因是因为2.5.2不支持okhttp3，所以按照他的格式自己写一个

这个项目用的kotlin，直接贴过去就行，java完全兼容

application中设置

        //初始化okhttp
        val sslParams = HttpsUtils.getSslSocketFactory(null, null, null)
        val okHttpClient = OkHttpClient.Builder()
                .sslSocketFactory(sslParams.sSLSocketFactory, sslParams.trustManager)
                .protocols(Collections.singletonList(Protocol.HTTP_1_1))
                .connectTimeout(10000L, TimeUnit.MILLISECONDS)
                .readTimeout(10000L, TimeUnit.MILLISECONDS)
                .build()
        OkHttpUtils.initClient(okHttpClient)


        //Picasso 支持https
        val picasso = Picasso.Builder(this)
                .downloader(MyDownloader(okHttpClient))
                .build()
        Picasso.setSingletonInstance(picasso)

MyDownloader.kt

package com.cyyz.mobilesignature.utils

import android.net.Uri
import com.squareup.picasso.Downloader
import com.squareup.picasso.NetworkPolicy
import okhttp3.CacheControl
import okhttp3.OkHttpClient
import okhttp3.Request
import java.io.IOException

/**
 * Created by TaoYuan on 2017/11/8 0008.
 */

private class MyDownloader(client: OkHttpClient) : Downloader {
    private var client: OkHttpClient? = null

    init {
        this.client = client
    }

    @Throws(IOException::class)
    override fun load(uri: Uri, networkPolicy: Int): Downloader.Response {

        var cacheControl: CacheControl? = null
        if (networkPolicy != 0) {
            if (NetworkPolicy.isOfflineOnly(networkPolicy)) {
                cacheControl = CacheControl.FORCE_CACHE
            } else {
                val builder = CacheControl.Builder()
                if (!NetworkPolicy.shouldReadFromDiskCache(networkPolicy)) {
                    builder.noCache()
                }
                if (!NetworkPolicy.shouldWriteToDiskCache(networkPolicy)) {
                    builder.noStore()
                }
                cacheControl = builder.build()
            }
        }

        val builder = Request.Builder().url(uri.toString())
        if (cacheControl != null) {
            builder.cacheControl(cacheControl)
        }

        val response = client!!.newCall(builder.build()).execute()
        val responseCode = response.code()
        if (responseCode >= 300) {
            response.body().close()
            throw Downloader.ResponseException(responseCode.toString() + " " + response.message(), networkPolicy,
                    responseCode)
        }

        val fromCache = response.cacheResponse() != null

        val responseBody = response.body()
        return Downloader.Response(responseBody.byteStream(), fromCache, responseBody.contentLength())

    }

    override fun shutdown() {

        val cache = client!!.cache()
        if (cache != null) {
            try {
                cache.close()
            } catch (ignored: IOException) {
            }

        }
    }
}