We consider a linear quadratic stochastic optimal control problem with bounded convex control constraint. Instead of reformulating the original problem into a fully coupled nonlinear forward-backward stochastic differential equation, we shall use the variational inequality theory to establish an iterative algorithm for solving the stochastic optimal controls. The main advantage of our approach is that, in each step, we only need to solve numerically an uncoupled forward-backward linear stochastic differential equation and we do not need to assume the optimal control is unique.