In this talk we introduce an iterative algorithm based temporal splitting for optimal control of linear parabolic equation. The algorithm is based on splitting the whole time interval into subintervals which are associated with suitable coupling conditions. We then apply some numerical method for time discretization in each subinterval. We prove the convergence for iterative solution through energy estimates between two subintervals. The convergence analysis reveals how the convergence rate depending on the coupling parameters. We show numerical experiments to illustrate the algorithm.