In this talk, we develop error estimates for discretization of stochastic linear quadratic problems governed by stochastic heat equations. The discretization is given by finite element method in space and implicit Euler method in time. After obtaining the convergence rate for discretization of associated forward-backward heat equations, we provide the error estimates of optimal control for aforementioned discretization of SLQ problems, which is 1-order in space and 1/2-order in time.