Summary: We investigate the existence of the solution of variational inequality problems by applying the Bregman generalized projection operator defined on a nonempty, closed and convex subset \(C\) of a Banach space \(E\) with dual space \(E^\ast\). We first prove some properties, including the continuity property, of the Bregman generalized projection operator. Then we drive necessary and sufficient conditions for the existence of the solution of the variational inequality problems by employing the well-known KKM-theorem. Finally, we investigate the approximation of the solution of the variational inequality by a Mann type iterative scheme. Our results improve and generalize many known results in the current literature.