Holographic stereogram printing technology is a widely used holographic technology. In recent years, our project team has proposed a new method to preprocess the perspective images and print the holographic stereograms, called as the effective perspective image segmentation and mosaicking (EPISM) method, in which the holographic printing effect can be achieved via one-step recording beyond the traditional two-step recording, and thus it possesses high research value. In order to predict the printing results of holographic stereograms based on the EPISM method before optical experiments, a numerical algorithm for the reconstruction of holographic stereograms after EPISM is proposed. This algorithm performs a numerical reconstruction of synthetic perspective images processed by the EPISM method and the reproduced images seen at different viewing angles and viewing positions prior to optical printing can be pre-obtained. Through the comparison among the original sampling images, the numerically reconstructed images and the experimentally reproduced images, it is found that the proposed algorithm can be used to simulate the optical experimental results of holographic stereogram printing with the EPISM method.