In telescopic systems consisting of Alvarez lenses, chromatic aberrations vary with the magnifications and the fields of view. Computational imaging has developed rapidly in recent years, therefore we propose a method of optimizing the DOE and the post-processing neural network in 2 stages for achromatic aberrations. We apply the iterative algorithm and the gradient descent method to optimize the DOE, respectively, and then adopt U-Net to further optimize the results. The results show that the optimized DOEs improve the results, the gradient descent optimized DOE with U-Net performs the best and has a very robust and good performance in the case of simulated chromatic aberrations. The results also verify the validity of our algorithm.