In this paper, a two-step optical design method is proposed to build a superior Fresnel-based photovoltaic concentrator for enhancing light conversion efficiency with the multi-junction solar cell. In the first step, we orthogonally segment a traditional Fresnel concentrator and remove the two normal stripe bands around the horizontal and vertical axes, as well as recombine the resultant four quadrants again. By using such a specific Fresnel concentrator design, a square light pattern can be constructed owing to the off-axis non-rotational symmetric superposition of light. In the second step, as for the response wavelengths of a specific triple-junction solar cell, we further carry out a triple-wavelength and multi-focus design of the above Fresnel concentrator for improving the uniformity of light distribution on the solar cell. To show the validity of this novel design method, a solar concentrator, with typical design parameters including the geometrical concentration ratio of 800x and the F-number of 0.775, is designed and simulated. As a result, theoretical irradiance uniformity up to 87% is obtained. In addition, considering the fact that no second optical element is involved in the concentrator system, our design method inherently has the advantages of good compactness, high efficiency, low cost, and ease for mass-production. We believe that such a concentrator is of great significance to solar cells for high conversion efficiency of light in the concentrator photovoltaic system. (C) 2019 Optical Society of America