In this paper, we study a modification of the Golden Ratio Algorithm (GRAAL) for solving monotone variational inequalities. We present an inertial Bregman modification of GRAAL for solving the aforementioned problem. Our proposed algorithm contains the inertial technique, the Bregman distance and a fully adaptive stepsize. We present a convergence result when the cost operator is monotone and locally Lipschitz continuous. Furthermore, we obtain the sublinear rate of convergence of our proposed method. Finally, we present numerical experiments to illustrate the applicability of our proposed method.