Abstarct: In this thesis, we solve a class of time-delayed optimal control problems using neural network. In the first chapter, we introduce to introduction and neural network and the needed definitions. In the second chapter, we study Bolza optimal control problems with time-delayed. The problem is first transformed, using a Pade approximation, to one without a time-delayed argument. Then we approximate it using neural network. Numerical results are also given for six test examples. The third chapter consists of infinite-horizon time-delayed optimal control problem. The problem is first transformed, using a Pade approximation, to one without a time-delayed argument. Then by a suitable change of variable, we transformed the obtained non-delay optimal control problem to a finite-horizon optimal control problem. We solve it numerically using neural network. Numerical results are also given for two test examples.