In this paper,a novel method for the factorization of a tensor with missing dat a is proposed for higher-order data inpainting.The proposed method enforces nonnegativity on core tensor and factor matrices,while sparseness on core tensor in Tucker factorization,and alternating proximal gradient method (AP GM) can be used for minimizing the modified Tucker function.Numerical experiments are conducted in medical magnetic resonanc e imaging (MRI) images,color images and videos,and the simulation results demonstrate that the proposed inpainting method outperforms t he state-of-art tensor factorization and tensor completion based methods.It achieves higher performance in terms o f peak signal to noise ratio (PSNR),structural similarity index measurement (SSIM) and root mean square error (RMSE).