In this paper, we propose a novel nonlinear 3D image correlator using a fast computational integral imaging reconstruction (CIIR) method. In order to implement the fast CIIR method, the magnification process was eliminated. In the proposed correlator, elemental images of the reference and target objects are picked up by lenslet arrays. Using these elemental images, reference and target plane images are reconstructed on the output plane by means of the proposed fast CIIR method. Then, through nonlinear cross-correlations between the reconstructed reference and the target plane images, the pattern recognition can be performed from the correlation outputs. Nonlinear correlation operation can improve the recognition of 3D objects. To show the feasibility of the proposed method, some preliminary experiments are carried out and the results are presented by comparing the conventional method.