We consider a general quasi-variational inequality problem involving nonlinear, nonconvex and nondifferentiable term in uniformly smooth Banach space. Using retraction mapping and fixed point method, we study the existence of solution of general quasi-variational inequality problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-variational inequality problem. The theorems presented in this paper generalize, improve, and unify many previously known results in the literature.