Light field salient object detection (SOD) is an essential research topic in computer vision, but robust saliency detection in complex scenes is still very challenging. We propose a new method for accurate and robust light field SOD via convolutional neural networks containing feature enhancement modules. First, the light field dataset is extended by geometric transformations such as stretching, cropping, flipping, and rotating. Next, two feature enhancement modules are designed to extract features from RGB images and depth maps, respectively. The obtained feature maps are fed into a two-stream network to train the light field SOD. We propose a mutual attention approach in this process, extracting and fusing features from RGB images and depth maps. Therefore, our network can generate an accurate saliency map from the input light field images after training. The obtained saliency map can provide reliable a priori information for tasks such as semantic segmentation, target recognition, and visual tracking. Experimental results show that the proposed method achieves excellent detection performance in public benchmark datasets and outperforms the state-of-the-art methods. We also verify the generalization and stability of the method in real-world experiments.