Mask-based lensless imaging cameras have many applications due to their smaller volumes and lower costs. However, due to the ill-nature of the inverse problem, the reconstructed images have low resolution and poor quality. In this article, we use a mask based on almost perfect sequence which has an excellent autocorrelation property for lensless imaging and propose a Learned Analytic solution Net for image reconstruction under the framework of unrolled optimization. Our network combines a physical imaging model with deep learning to achieve high-quality image reconstruction. The experimental results indicate that our reconstructed images at a resolution of 512 × 512 have excellent performances in both visual effects and objective evaluations.