MRI reconstruction based on supervised learning methods, have achieved remarkable success. However, because of the difficulty and high cost of the MR images collection process, it is not always easy to obtain a big dataset with strong supervised information. Therefore, weakly supervised learning will be a possible solution. In this work, we proposed a weakly deep prior learning algorithm to train a complex UNet for multi-coil MR images reconstruction without very precise labels. The result shows that our proposed algorithm can provide a competitive performance compared to the classical methods with enoucraging quantitative indicators of SSIM and PSNR.