We propose a design method of a free-form reflector for collimating illumination of integrating spherical light sources to reduce the space occupation on a satellite. By using this method, a square irradiance distribution with large area can be achieved through a integrating sphere with small diameter. Firstly, the mathematical model of off-axis reflection lighting of free-form surface is established through the point light source model, then the free-form surface is discretized by Chebyshev points, and the free-form surface model that satisfies the point light source illumination is solved. Finally, the light source characteristics of the integrating sphere are analyzed. The transformation from the point light source illumination model to the integrating sphere illumination model is achieved by the optimization of the free-form surface energy distribution. The analysis results show that when the illumination area is set as 140 mm×140 mm, the irradiance non-uniformity of the target surface is less than 0.02. This method can meet the requirements of spaceborne calibration for light weight, short light path and simple structure.