In this work, an array optical tweezer system based on non-orthogonal binary phase plates is proposed. The proposed system can stably trap multiple particles arranged in a non-orthogonal array. The binary phase is designed through a genetic algorithm and the Fourier transform theory of a high numerical aperture (NA) objective lens under tight focusing conditions. The normalized phase turning point of the binary phase is optimized to have different beam-splitting ratios, high diffraction efficiency, and high uniformity, and then it can be used to design the non-orthogonal binary phase plate with different inclination angles. Using this binary phase plate, we can obtain a variety of non-orthogonal array spots in the focal plane of the high-NA objective lens. Furthermore, the stable trapping of silica microspheres can be realized in the experiment of optical tweezers based on the non-orthogonal array spots. Theoretical simulation and experimental results show that this method can effectively achieve the optical trapping of a non-orthogonal arrangement of a large number of particles. This technology is expected to play an essential role in the epitaxial growth of nanoparticle arrays.