To improve the nonlinear approximating ability of cerebellar model articulation controller(CMAC), by introducing the Gauss basis functions and the similarity measure based addressing scheme, a new kind of fuzzy CMAC with Gauss basis functions(GFCMAC) was presented. Moreover, based upon the improvement of the self organizing feature map algorithm of Kohonen, the structural self organizing algorithm for GFCMAC(SOGFCMAC) was proposed. Simulation results show that adopting the Gauss basis functions and fuzzy techniques can remarkably improve the nonlinear approximating capacity of CMAC. Compared with the traditional CMAC,CMAC with general basis functions and fuzzy CMAC(FCMAC), SOGFCMAC has the obvious advantages in the aspects of the convergent speed, approximating accuracy and structural self organizing.