In order to improve the utilization efficiency of the radio resources, the spatial frequency multiplexing is considered in an OFDMA-based cognitive radio system. The conflict between the cognitive radio links over sub-carriers is described by interference criteria and adjacency matrix, thus the optimization problem to maximize the sum-rate of secondary networks is modeled as a multi-winner sub-carrier auction game which is based on VCG (Vickrey-Clarke-Groves) mechanism, the optimal solution can be obtained by solving a binary integer programming for each of the sub-carriers. Numerical results show that the proposed sub-carrier auction game can effectively improve the utilization efficiency of the resources for cognitive radio networks.