A new kind of micro-structured core photonic crystal fiber with a rectangular array of ten air holes in the core region and the incremental cladding is proposed. Using the finite element method, the fundamental mode field, birefringence, confinement loss and dispersion characteristics are investigated simultaneously by changing the radii and pitches of the air holes in the core. Numerical results show that the birefringence and confinement loss are respectively about 3.22×10-2 and 4.92×10-8 dB/m at 1.55 μm when the small air hole radius is 0.225 μm and the cladding air hole pitch size is 1.30 μm, and three corresponding zero dispersion points can be obtained over the wavelength range from 0.6 μm to 2.0 μm. In addition, the largest birefringence can reach up to 3.45×10-2 and the confinement loss reduces down to 2.88×10-9 dB/m by optimizing the structural parameters. The proposed photonic crystal fiber has a broad prospect of applications in fiber-optic communications, fiber optic sensing and other fields.