Correntropy based algorithms are widely used in non-Gaussian signal processing, but they also suffer from the conflict between the step size and the misadjustment. In order to solve this problem, a convex combination filter based on maximum correntropy criterion(CMCC) was proposed to obtain the fast convergence speed of the filter with large step size as well as the low misadjustment of the filter with small step size. However, the convex combination of two filters with different step sizes will result in the penalties in terms of the combined filter′s convergence speed and the ability to track the optimal value. In this paper, a multi-convex combination filter based on maximum correntropy criterion(MCMCC) is proposed to provide more adaptive filters with different step sizes, so that the weight ratio can be flexibly adjusted for more step sizes, and thus having better tracking ability. Simulation results show that compared with the CMCC algorithm, the proposed MCMCC algorithm has faster convergence speed, stronger re-convergence performance and better tracking ability in the system identification for in the presence of mixed Gaussian noise and abrupt change.