A deterministic entanglement purification protocol (EPP) for polarization decohered Greenberger-Horne-Zeilinger (GHZ) state is presented based on linear optical elements such as polarization beam splitter and half-wave plate. The proposed EPP makes use of spatial entanglement as an additional resource to purify polarization entanglement, and its essence is to transfer the bit-flip and phase-flip errors from polarization degree of freedom (DOF) to spatial one using the methods of linear optics and hyper-entanglement. The entanglement purification scheme can be implemented without knowing any parameters of the low-entanglement GHZ state to be purified, without converting phase flip errors to bit flips for purification, introducing the nonlinear effects. According to the proposed EPP, just in a purification step, both the bit-flip and phase-flip errors in the polarization mixed states can be deterministically corrected by using additional entanglement DOF in spatial mode, which greatly enhances the experimental feasibility of this scheme.