Computational integral imaging method can digitally provide a series of plane images of three-dimensional (3D) objects. However, the resolution of 3D reconstructed images is dramatically degraded as the distance from the lenslet array increases. In this paper, to overcome this problem, we propose a novel computational integral imaging reconstruction (CIIR) method based on smart pixel mapping (SPM). Since SPM is a computational process in which elemental images recorded at long distances are convertible to ones recorded near lenslet array, this can give us the improved resolution of plane images for 3D objects located at a long distance range from a lenslet array. For the effective use of the SPM-based CIIR method, we design a novel two-stage CIIR method by the combined use of the conventional CIIR and the SPM-based one. The conventional CIIR method is applied over a short distance range, while the SPM-based CIIR is used over a long distance range. We carry out some experiments to verify the performance of the two-stage CIIR system. From the experimental results, the proposed system can provide a substantial gain over a long distance range in terms of the resolution of reconstructed plane images.