The Letter introduces a novel filtering method based on convolutional neural networks (CNNs) for quality enhancement of light field (LF) images captured by a plenoptic camera and compressed using high-efficiency video coding (HEVC). The method takes advantage of the macro-pixel (MP) structure specific to the LF images and proposes a novel MP-wise filtering approach based on a novel deep neural network architecture. The proposed CNN-based method achieves an outstanding performance when HEVC is employed without its in-loop filters. Experimental results show high luminance-peak signal-to-noise ratio (Y-PSNR) gains and average Y-Bjøntegaard delta (BD)-rate savings of 25.6% over HEVC on a large data set.