In this paper, a fast numerical reconstruction of the integral imaging based on a determined interval mapping is proposed. To reduce the computation time, the proposed method employs the determined interval mapping instead of the use of magnification. In the numerical reconstruction procedure, the acquired elemental image array (EIA) from the 3D object is displayed. The flipped elemental image (EI)s are numerically formed by the virtual pinhole array. Then, the determined interval depending on the reconstruction plane is calculated and applied to each flipped EI. These flipped EIs are shifted to match the determined interval at the reconstruction plane and superimposed together. After this superimposed image is divided by the number of the superposition, the position error between the location of the shifted EI and the pixel position of the reconstruction plane is corrected by interpolation. As a result, the refocused image depending on the reconstruction plane can be reconstructed rapidly. From the experimental result, we confirmed that the proposed method largely decreased the computation time compared with the conventional method. In addition, we verified that the quality of the reconstruction by the proposed method is higher than the conventional method by the use of the structural similarity index method.