Dual-layer displays (DLDs) can achieve high dynamic range by reducing light leakage via bonding two LC panels. However, the physical distance between the two LC panels introduces a parallax error when the display is viewed off-axis. This paper proposes a convolutional neural network-based image splitting algorithm for improving the display quality of a DLD. In order to improve processing speed, the network structure is designed relatively simply. The training dataset is established mainly based on TV signals. Different from the common image evaluation metrics based on PSNR and SSIM, the paper proposes to apply learned perceptual image patch similarity (LPIPS) to define the loss function for DLDs. The simulation and experiment results show that compared with the existing method, the proposed method has better performance in reducing parallax error and improving image details. The processing time can be shortened by 2.7 times. The proposed CNN-based method can greatly reduce the processing time while maintaining high display quality, which presents high practicability.