A square-lattice photonic crystal fiber with gradually increasing air-holes in a silica matrix is analyzed numerically based on a full-vector finite element method with quadratic order triangular elements, and an anisotropic perfectly matched layer is also employed as a boundary condition at computational window edges. The mode distribution, confinement loss and birefringence of the fundamental mode in the fiber are simulated in details. It is confirmed from numerical results that low confinement loss of 1.31×10－6 dB/m can be realized under condition of four arrays of air holes in the photonic crystal fiber, and high birefringence can be obtained through adjusting the diameter of inner-ring air holes in the fiber, which is more obvious in the longer wavelength range. The numerical results are highly instructive for the fabrication of birefringent photonic crystal fibers.