The novel rotating rectangular aperture (RRA) system provides a good solution for space-based, large-aperture, high-resolution imaging tasks. Its imaging quality depends largely on the image synthesis algorithm, and the mainstream multi-frame deblurring approach is sophisticated and time-consuming. In this paper, we propose a novel full-aperture image synthesis algorithm for the RRA system, based on Fourier spectrum restoration. First, a numerical simulation model is established to analyze the RRA system’s characteristics and obtain the point spread functions (PSFs) rapidly. Then, each image is used iteratively to calculate the increment size and update the final restored Fourier spectrum. Both the simulation’s results and the practical experiment’s results show that our algorithm performs well in terms of objective evaluation and time consumption.