In this paper, we propose new symmetric cost functions for global stereo methods. We first present a symmetric data cost function for the likelihood and then propose a symmetric discontinuity cost function for the prior in the MRF model for stereo. In defining cost function, both the reference image and the target image are taken into account to improve performance without modeling half-occluded pixels explicitly and without using color segmentation. The performance improvement of stereo matching due to the proposed symmetric cost functions is verified by applying the proposed symmetric cost functions to the belief propagation (BP) based stereo method. Experimental results for standard testbed images show that the performance of the BP based stereo method is greatly improved by the proposed symmetric cost functions.