According to the optical properties of lenticular lens array, we build a virtual image display platform for one-dimensional integral imaging. Then we analyze systematically the display resolution, the viewing angle and the depth of focus, which can describe the display characteristics. Based on this, a novel method is proposed for reconstructing the viewpoint image during the one-dimensional integral imaging display process by computer simulation. According to the laws of light propagation in lenticular lens, the images, seen from some viewpoint, corresponding to every lenticular lens can be obtained and used to make up a viewpoint image using the proposed method. Experiment results show that the obtained viewpoint image can perfectly match that from the display platform and truly describe the one-dimensional integral imaging display process. The obtained parameters of the display characteristics can be used as the theoretical basis when designing one-dimensional integral imaging system.