Aimed at the problems that the blind equalization algorithm does not require a sequence and can effectively reduce intersymbol interference, but under the impulse noise environment, the existing single filter equalization algorithm fails to effectively balance the convergence rate and steady state error, and fails to effectively reduce ISI, a convex combination blind equalization algorithm is proposed based on cosine cost function. The algorithm utilizes two blind equalizers in parallel ( one as a fast filter ) for guaranteeing the convergence rate and ( the other as a slow filter) for reducing the equalization error. In order to further reduce the impact of impulse noise, the fractional loworder statistic is introduced into the blind equalization algorithm based on the cosine cost function and the blind equalization algorithm based on the decisiondetection algorithm. These two algorithms are used as weight vector update algorithms for fast and slow filters, respectively. The simulation results show that when the noise is set to Gaussian white noise of 28 dB, the ISI of the new algorithm will be lower than CMA and CCF and the constellation diagram is also clear. When the noise environment is 28 dB α stable distribution noise, the new algorithm uses the fractional loworder statistic to suppress the impulse noise to obtain lower ISI and clear constellation, and the convex combination structure takes into account the steadystate error and convergence rate, further reducing the steadystate error while ensuring a faster convergence rate.