This paper proposes an adaptive critic design (ACD) based control method of a generator in a single machine infinite bus (SMIB) power system, by using a biologically-inspired artificial neural network (BIANN). A heuristic dynamic programming (HDP) based optimal controller applying three BIANNs is designed for the control of the turbo generator in the SMIB system. By developing a numerical derivative calculation algorithm, the difficulties in back-propagating errors through a BIANN are overcome. The HDP-BIANN controller for the turbo generator in the SMIB system is trained and run online for different operating conditions. The results show that the HDP-BIANN controller improves the system damping as well as dynamic transient stability more effectively than the conventional controllers (CONVC) for not only small step changes, but also large disturbances such as a three phase short circuit. This is the first time that a BIANN is used for closed-loop optimal control of a power system.