The sparse representation of wireless channels is of great significance for studying channel estimation. However, the existing sparse representation of wireless channel mostly adopts a fixed sparse basis function. The sparse representation will not be performed well when the channel environment is complex. In this paper, a novel sparse representation method for wireless channels based on the modified Takenaka-Malmquist Basis (MTMB) functions is proposed. The representation of the wireless channels is firstly made using a limited number of Takenaka-Malmquist Basis (TMB) function combinations. Further, we modify the TMB function to match the channel model of the desired sparse representation. In addition, in order to make the MTMB functions fit the sparsity model better, the obtained MTMB dictionary is trained by the K-SVD algorithm. Therefore, the sparse representation of the wireless channel can be obtained by these public modified Takenaka-Malmquist Basis (PMTMB) functions. Simulation results show that PMTMB are able to match the wireless channels structure well and can achieve high accurate performance of sparse representation.