In this paper we present the solution to the algebraic Riccati-type equation of the state-dependent noise linear-quadratic optimal control problem in terms of algebraic Lyapunov iterations. By properly initializing the sequence of algebraic Lyapunov iterations we got monotonic convergence from above to the positive-definite stabilizing solution of the algebraic Riccati-type equation (the solution that represents the optimal solution to the corresponding optimal control problem). The proposed algorithm requires much less computational efforts than those previously used to solve the same problem.