We proposed a two-step approach to evaluate automatically liver MR image quality. Firstly, we used a U-Net to segment the liver region. Then image patches were extracted from this region and another CNN was applied to estimate the quality of each image patch. The quality of the entire image was calculated based on the total percentage of 'bad' image patches in all patches. Receiver operating characteristic curve and confusion matrix were used to evaluate the performance of the proposed method. The performance of our method was comparable to human image readers.