<p>This paper is concerned with the error estimate of optimal controls for the time optimal control problem with the heat equation by finite element approximation. The finite element discretization is applied both for the state space and the control space. Due to the lack of the unique continuation property for the discrete equation, the expression of the discrete optimal control can not be obtained directly by Pontryagain’s maximum principle. With the aid of uniform convergence of the adjoint state in some sense, the discrete optimal control can be expressed. On this basis, the error estimate of optimal controls is established without any assumptions. Moreover, error estimates of states and adjoint states are also obtained.</p>