In this talk we introduce an iterative algorithm for solving a class of optimal control problems constrained by time-periodic heat equation, where the optimization is concerned by searching a best source term of the heat equation to minimize the objective function. By applying the optimality condition, the problem is firstly transformed into two coupled time-period heat equations. Then iterative algorithm is applied to decouple the PDE system. Finally, the equations are separately solved in the Gauss-Seidel pattern. Numerical examples are presented to illustrate the robustness of convergence rate of the algorithm with respect to the discretization parameters.