In this paper, we propose a computational integral imaging reconstruction (CIIR) method by use of image interpolation algorithms to improve the visual quality of 3D reconstructed images. We investigate the characteristics of the conventional CIIR method along the distance between lenslet and objects. What we observe is that the visual quality of reconstructed images is periodically degraded. The experimentally observed period is half size of the elemental image. To remedy this problem, we focus on the interpolation methods in computational integral imaging. Several interpolation methods are applied to the conventional CIIR method and their performances are analyzed. To objectively evaluate the proposed CIIR method, we introduce an experimental framework for the computational pickup process and the CIIR process using a Gaussian function. We also carry out experiments on real objects to subjectively evaluate the proposed method. Experimental results indicate that our method outperforms the conventional CIIR method. In addition, our method reduces the grid noise that the conventional CIIR method suffers from.