Use okio to zip file.

ZipUtils.java

import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;

import okio.BufferedSink;
import okio.BufferedSource;
import okio.GzipSink;
import okio.Okio;

public class ZipUtil {

    public static void zip(File source, File dest) throws IOException {
        BufferedSource bufferedSource = null;
        BufferedSink bufferedSink = null;

        try {
            bufferedSource = Okio.buffer(Okio.source(source));
            bufferedSink = Okio.buffer(new GzipSink(Okio.sink(dest)));

            int length;
            byte[] buf = new byte[8192];
            while ((length = bufferedSource.read(buf, 0, buf.length)) != -1) {
                bufferedSink.write(buf, 0, length);
            }
        } finally {
            IoUtils.closeQuietly(bufferedSource);
            IoUtils.closeQuietly(bufferedSink);
        }
    }

}