Based on the birefraction of crystals and phase retardation of wave plate, a 2  ×  4 90-deg crystal spatial optical hybrid is designed. It is comprised of three birefringent optical plates, λ  /  4 wave plate and two λ  /  2 wave plates. By splitting and recombining the signal beam and local oscillator beam, four mixed beams with phase shift of 90 deg are obtained. The mathematical model of the mixer is established by Jones matrices. The results show that the hybrid has low insertion loss, and by rotating the wave plate, the phase difference and split ratio between in-phase and quadrature-phase can be changed. It proved that the crystal hybrid design method we proposed has good performance; the phase compensation and splitting ratio adjustment scheme is simple, effective, and feasible; and it can be applied to free-space coherent optical communication system well.