The Talbot effect of the square-aperture microlens array is studied theoretically and experimentally. The complex wave amplitude distribution of this array in the Fresnel diffraction field is analyzed with the optical transfer function to resolve the imaging situation of Talbot image. In the experiment, three alternating images appear at certain distances, and the experimentally measured imaging distance is consistent with the theoretical prediction. In addition, the Talbot sub-image imaging law is invariant when the parameters of the square-aperture microlens array change. The Talbot sub-image image elements overlap, when the center distance is between one and two aperture diameters. The clear Talbot sub-images with checkerboard-shaped distributions of the square-aperture microlens array are observed in the fractional Talbot planes. It will broaden the practical application of the square-aperture microlens array.