Seismic data interpolation is an essential procedure in seismic data processing. However, conventional interpolation methods may generate inaccurate results due to the simplicity of assumptions, such as linear events or sparsity. On the contrary, deep learning trains a deep neural network with a large dataset without relying on predefined assumptions. However, the lack of physical prior in the traditional pure data-driven deep learning frameworks may cause low generalization for different sampling patterns. Inspired by the project onto convex sets (POCS) framework, a new neural network is proposed for seismic interpolation, named POCS-Net. The forward Fourier transform, inverse Fourier transform, and the threshold parameter in POCS are replaced by neural networks that are independent in different iterations. The threshold is trainable in POCS-Net rather than manually set. A nonnegative constraint is imposed on the threshold to make it consistent with traditional POCS. POCS-Net is essentially an end-to-end neural network with priors of sampling pattern and a pre-defined iterative framework. Numerical results on 3D synthetic and field seismic datasets demonstrate the superiority of reconstruction accuracy of the proposed method compared to the traditional and natural image-learned POCS methods.