Computer holography is a technology that use a mathematical model of optical holography to generate digital holograms. It has wide and promising applications in various areas, especially holographic display. However, traditional computational algorithms for generation of phase-type holograms based on iterative optimization have a built-in tradeoff between the calculating speed and accuracy, which severely limits the performance of computational holograms in advanced applications. Recently, several deep learning based computational methods for generating holograms have gained more and more attention. In this paper, a convolutional neural network for generation of multi-plane holograms and its training strategy is proposed using a multi-plane iterative angular spectrum algorithm (ASM). The well-trained network indicates an excellent ability to generate phase-only holograms for multi-plane input images and to reconstruct correct images in the corresponding depth plane. Numerical simulations and optical reconstructions show that the accuracy of this method is almost the same with traditional iterative methods but the computational time decreases dramatically. The result images show a high quality through analysis of the image performance indicators, e.g., peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and contrast ratio. Finally, the effectiveness of the proposed method is verified through experimental investigations.