High-birefringence photonic crystal fiber (PCF) has many applications in fiber lasers, optical fiber communications and sensors, and is usually made by arranging asymmetrical air holes in its cross section. Though this design can obtain high birefringence in the fiber, it may lose the structural symmetry of mode field, and increase difficulty when connected to other fiber-optic devices. In this work, we propose a new design with a capability of having both high birefringence and good structural symmetry. Our design is based on a photonic quasi-crystal (PQC) fiber structure, in which air holes are arranged in an aperiodic order in the cladding. This kind of PQC fiber can introduce controllable birefringence into the fiber core and maintain certain symmetry of mode field. Using the full vector finite element method, we studied the mode field, birefringence, loss and nonlinear effect of the proposed PCF. It is shown that a birefringence coefficient of glt;1.5x10-2 can be obtained at 1.55 μm.