In order to further improve the convergence speed of the blind equalizer and reduce the steady-state error, a convex combination scheme for two constant modulus algorithm (CMA) blind equalization filters with different p and asynchronous length was proposed to be suitable for impulse noise environment subject to alpha stable distribution. The theoretical formula of excess mean square error (EMSE) of the scheme was derived by using fractional lower order statistics, energy conservation and separation hypothesis. Simulation results show that the scheme can retain the advantages of each component blind equalization filter, improve the convergence speed of the system to reduce the steadystate error, which verify the accuracy and rationality of the scheme.