In this study, a sub-aperture scanning Fourier transform system is proposed for performing the fast measurement of the bidirectional reflectance distribution function (BRDF). The sub-aperture scanning Fourier transform method that uses a single Fourier transform lens exhibits an expanded single-measurement field of view, a long working distance, and a low cost. Furthermore, the system is simple; thus, rapid and effective measurement of the BRDF can be realized over a large space frequency range. When compared with the angular subdivision spectroradiometer method, the proposed method exhibits higher sensitivity, accuracy, and detection speed. The scattered light field on the sample plane was evaluated through sub-aperture scanning, and numerical splicing was conducted in the Fourier space; the BRDF angle measurement range was expanded. Finally, the proposed method was verified based on the experimental data. The experimental results denote that the relative error between the proposed method and the angular subdivision spectroradiometer method is less than 1%. Further, the measurement time of the proposed method is 1/10 of that of the angular subdivision spectroradiometer method, and the system accuracy can become 0.005°. These results provide theoretical basis and technical support for the application of sub-aperture scanning Fourier transform systems in BRDF measurement.