A type of quasiperiod photonic crystal (QPC) that can achieve negative refraction is proposed. The QPC has 12-fold symmetry and consists of a quasiperiod array of air-holes arranged in a dielectric background. The propagation of electromagnetic wave across the 12-fold quasicrystal is investigated by employing finite difference time domain method. Simulation on the wedge-shaped sample demonstrates that negative refraction can occur in the quasicrystal structure. Parallel QPC slab is further designed to explore the influence of surface termination of flat slab on the propagation of electromagnetic wave. The results show that by changing the surface termination of flat slab, the electromagnetic field distribution behind the slab can be modulated. Under appropriate surface condition, focusing can be obtained by the QPC slab. As a result, proper surface parameter should be carefully chosen for practical applications.