In this paper, we consider the general variational inequality GVI(F, g, C), where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We suggest and analyze a new modified hybrid steepest-descent method of type method $u_{n+l}=(1-{alpha}+{ heta}_{n+1})Tu_n+{alpha}u_n-{ heta}_{n+1g}(Tu_n)-{lambda}_{n+1}{mu}F(Tu_n),;n{geq}0$. for solving the general variational inequalities. The sequence ${x_n}$ is shown to converge in norm to the solutions of the general variational inequality GVI(F, g, C) under some mild conditions. Application to constrained generalized pseudo-inverse is included. Results proved in the paper can be viewed as an refinement and improvement of previously known results.