We propose a three-dimensional (3D) image encryption method based on the modified computational integral imaging (CII) technique with the smart pixel mapping (SPM) algorithm, which is introduced for reconstructing orthoscopic 3D images with improved image quality. The depth-converted two-dimensional (2D) elemental image array (EIA) is firstly obtained by SPM-based CII system, and then the 2D EIA is encrypted by Fibonacci transform for 3D image encryption. Compared with conventional encryption methods based on integral imaging (II), the proposed method enables us to reconstruct orthoscopic 3D images at long distance. In addition, the qualities of the reconstructed plane images are enhanced by applying the SPM and pixel average algorithm (PAA) in CII. To show the usefulness of the proposed method, we carry out the preliminary experiments and present the experimental results.