The traditional sparse adaptive filtering has the problems of poor steady-state performance and even unable to converge in impulse noise interface environment. In order to solve the problems and improve the accuracy of sparse parameter identification without increasing too much computational cost， a sparse adaptive filtering algorithm based on Generalized Maximum Versoria Criterion （GMVC） was proposed， namely the GMVC with CIM constraints （CIMGMVC）. Firstly， the generalized Versoria function was employed as the learning criterion， which contained the reciprocal form of the error p-order moment. And thus the purpose of suppressing impulse noise was able to be achieved because the GMVC would approach to 0 when the error caused by the impulse interference was very large. Then， a novel cost function was constructed by combining the Correntropy Induced Metric （CIM） used as the sparse penalty constraint and the GMVC， where the CIM was based on the Gaussian probability density function， and it was able to be infinitely close to l_{\mathrm{0}} -norm when the appropriate kernel width was selected. Finally， the CIMGMVC algorithm was derived by using the gradient method， and the mean square convergence of the proposed algorithm was analyzed. The simulation was performed on Matlab platform， and the \alpha -stable distribution model was used to generate impulse noise. Experimental results show that， the proposed CIMGMVC algorithm can effectively suppress the interference of non-Gaussian impulse noise， it has the better robustness than the traditional sparse adaptive filtering， and has the steady-state error lower than the GMVC algorithm.