A novel hexagonal honeycomb lattice photonic crystal fiber is proposed, which is composed of a central defect core, a cladding with elliptical air-hole and small round air-holes. Based on the full vector finite element method with anisotropic perfectly matched layers, its birefringence, dispersion, nonlinearity, leakage loss and mode field are numerically investigated. We compare hexagonal honeycomb lattice photonic crystal fiber and hexagonal elliptical lattice photonic crystal fiber, both of which have the same structure parameters. Numerical results indicate that the proposed fiber shows high birefringence and negative dispersion effect. The birefringence is 1.02× 10-2, both its dispersion and dispersion slope are negative, the dispersion slope values are between -0.132- -0.121 ps·km-1·nm-2 over C band, the leakage loss is close to 102 dB·m-1 and the non-linear coefficient is 45.7 km-1·W-1 at a wavelength of 1.55 μm, if the parameter is selected as Λ =1.15 μm, η =0.5, f=0.48, and d1=0.4 μm. It is found that the hexagonal honeycomb lattice photonic crystal fiber easily obtains high birefringence, large negative dispersion and low non-linear coefficient. It is demonstrated that the hexagonal honeycomb lattice photonic crystal fiber has huge potential in designing dispersion compensation photonic crystal fiber.