In this paper, we introduce a new iterative algorithm with Bregman distance approach for approximating a common solution of a finite family of Mixed Equilibrium Problem (MEP) with a relaxed monotone mapping and a countable family of Bregman multi-valued quasi-nonexpansive mappings in a reflexive Banach space. Under standard and mild assumption of relaxed monotonicity of the MEP associated mapping, we establish the strong convergence of the iterative sequence. A numerical example is presented to illustrate the performance of our method. The results obtained in this work extend and complement many related results in literature.