In this paper, a globally convergent proximal gradient method is developed for convex multi-objective optimization problems using Bregman distance. The proposed method is free from any kind of a priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a descent direction. This subproblem uses a Bregman distance induced by a strongly convex function. An Armijo type line search is conducted to find a suitable step length. A sequence is generated using the descent direction and step length. It is justified that this sequence converges to a weak efficient solution under some mild assumptions. The method is verified and compared with one existing method using a set of test problems.