To solve the direction of arrival (DOA) estimation problem under impulsive noise modeled by Alpha-stable distribution, a robust MUSIC-like DOA estimator based on maximum mixture correntropy criterion (MMCC) is pr-posed in this paper. In this technique, the DOA estimation problem is transformed into an optimization problem with optimal step sizes. Since MMCC involves multiple kernel functions with different kernel sizes, it relies less on parameter selection. Experiments are carried out to demonstrate that the proposed MMCC-MUSIC out-performs several other DOA methods with different parameter values under noise conditions, including a changing GSNR and a changing characteristic exponent.