In this paper a square-lattice photonic crystal fiber with gradually increasing air-holes in a silica matrix has been put forward for the first time. The model field, dispersion, birefringence and confinement loss of the fibre fundamental mode are simulated by multipole method. It is found that low confinement loss can be realized under condition of fewer rings of air holes. Simulation shows that birefringence and dispersion of this square-lattice PCF are dominated by inner-ring air holes in the fibre. The simulation results of this paper are highly instructive for the fabrication of birefringent photonic crystal fibers.