In a traditional Fourier ptychography microscopy (FPM) system, multiple low-resolution (LR) intensity images have to be sequentially captured under variable illumination angles and then stitched together in the Fourier domain, which is time-consuming. This paper proposes a sparse aperture arrangement method in which the relationship between the spatial spectrum distribution and the light-emitting diodes array sampling pattern is investigated. Mathematical models of the proposed method are developed, and numerical simulations and optical experiments are demonstrated to verify its feasibility. The results show that the number of LR images could be decreased significantly without sacrificing image reconstruction quality. To the best of our knowledge, this is the first time that the sparse aperture arrangement has been exploited for FPM. The proposed method may provide new insights for improving the efficiency of the FPM platform and discovering more applications in digital pathology.