Summary: The general mixed variational inequality containing a nonlinear term is a useful and an important generalization of variational inequalities. The projection method cannot be applied to solve this problem due to the presence of the nonlinear term. To overcome this disadvantage,

*M. A. Noor* [Appl. Math. Comput. 141, No. 2–3, 529–540 (2003;

Zbl 1030.65072)] used the resolvent equations technique to suggest and analyze an iterative method for solving general mixed variational inequalities. In this paper, we present a new self-adaptive iterative method which can be viewed as a refinement and improvement of the method of Noor. Global convergence of the new method is proved under the same assumptions as Noor’s method. Some preliminary computational results are given.