In the fields of astronomical observation and fluorescence microscopic imaging, the obtained image is usually degraded by blur effects and Poisson noise. In this paper, we propose a robust hybrid regularization method consisting of total variation and L0-norm of image gradients and combine it with the Poisson distribution to formulate this kind of ill-posed problem. We also propose an efficient alternately minimization algorithm based on variable splitting and Lagrange multipliers to find the optimal solution, which can transform the original problem into a regularized deconvolution problem with quadratic fidelity term and a simple convex optimization problem. In the end, we carry out experiments to prove its convergence and effectiveness, the results show that the proposed method is stable, efficient and the quality of the restored image is comparable with some state-of-the-art methods.