Tandem microlens arrays are commonly used in many applications for the beam shaping of an arbitrary input intensity distribution into a top hat. Because of the periodic structure of the regular arrays, the output intensity distribution is modulated by equidistantly located sharp intensity peaks, which reduces the homogeneity of the beam. A new concept is proposed in this paper for tandem microlens arrays incorporating a center off-axis microlens array for the generation of an intensity far-field distribution with improved homogeneity under coherent illumination with the envelope of a top hat. The geometric centers of the sub-apertures are randomly offset by the light axis of the sub-lens in the array to break the periodicity. The influences of the various off-axis amounts on the homogeneity are discussed. The center off-axis microlens array has been fabricated, and the corresponding laser beam homogenizing experiment has been carried out. The results verify that a high homogeneity output intensity distribution can be achieved based on the presented method.