Abstract: We introduce and study a new generalized nonconvex variational inequalities.By using the projection thchnique,we suggest and analyze a new iterative method for this generalized nonconvex variational inequalities.The new iterative method converge under certain mild conditions.As a consequence,the algorithm and results presented in the paper overcome deficient algorithms and results existing in the literature.Our results can also be viewed as a novel and important extension and improvement of the previously known results.