Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational inequality represented as a sum of \(L_q\) -Lipschitz monotone and \(L_p\) -Lipschitz generally non-monotone operators. We applied a special sliding version of the classical Extragradient method to this problem and obtain better convergence results. In particular, to achieve \(\varepsilon \) -accuracy of the solution, the oracle complexity of the non-monotone operator Q for our algorithm is \(\mathcal {O}\left( L_p^2/\varepsilon ^2\right) \) in contrast to the basic Extragradient algorithm with \(\mathcal {O}\left( (L_p+L_q)^2/\varepsilon ^2\right) \) . The results of numerical experiments confirm the theoretical findings and show the superiority of the proposed method.