Many applications like laser manufacturing, homogeneous illumination or laser-induced fluorescence spectroscopy require a uniform intensity distribution and variable size of laser beam. Conventional laser beam shapers have a homogeneous but fixed-size laser spot. In this paper, a continuous zoom beam shaper based on microlens array is designed. It is essentially a multi-channel Kohler illumination system consisting of two identical microlens arrays and a zoom lens group, which transforms a Guassian or other complex spacial intensity distributions to a uniform square distribution of variable size on the target plane. The continuous zoom beam shaper adopts mechanical compensated optical configuration. Cam curve of the continuous zoom beam shaper is smooth enough and avoids inflection point. Compared with conventional laser beam shapers, the continuous zoom beam shaper has high intensity uniformity, variable size of uniform distribution and low cost. The design method and optimum result of continuous zoom beam shaper are presented. As an example, a continuous zoom beam shaper with a zoom ratio of 3× and variable size of uniform square distribution from 4.12×4.12 mm2 to 12.36×12.36 mm2 , is designed. The zoom lens group consists of the front fixed group, zoom group, compensation group and the rear fixed group. Intensity uniformity of output beam is greater than 90% in different zoom stages. It satisfies the needs of laser applications.