Aiming at the requirements for multi-zero dispersion points and high birefringence of photonic crystal fibers, a new kind of photonic crystal fiber with rhombus air-core structure is composed of four air holes locate at four points of rhombus is proposed. By using the numerical analysis method based on the finite element, we simulate the dispersion and the birefringence characteristics of photonic crystal fiber, and obtain the relationships between dispersion and wavelength, dispersion and size of structure, birefringence and wavelength, birefringence and size of structure. Simulation results show that better birefringence can be obtained when the requirement of power is met. In addition, two zero dispersion points can be obtained when diameter d1 is 0.4 m or 0.6 m. The results are of significance for the further development of photonic crystal fiber with multi-zero dispersion points.