In order to study the decoherence process of quantum system and find the ways to delay it, in this paper we investigate the decoherence process under correlated depolarizing channels by calculating the evolution of norm coherence, relative entropy coherence and basis-independent coherence of the three initial states: special initial state, maximum coherent state and isotropic state. From the analytic results, numerical results and evolution images, it can be found that 1) completely correlated channels can suppress decoherence to a greatest extent,. 2) the time point at which maximum decoherence occurs is irrelevant to the degree of correlation, but system’s decoherence evolution behavior depends on it. 3)the correlation of depolarizing channels can reinforce the collective quantum coherence between subsystems, and an inequality relation of basis-independent coherence is proved in this system.