Neural network model predictive control has been widely used in the field of automatic control. However, the off-line training of the neural predictor and the appearance of disturbances and parameter variations, during the control phase, affect the system output by inducing steady state error. This paper tries to overcome this problem by proposing an adaptive deep neural network model predictive controller. To ensure the convergence of the adaptive process, we use Lyapunov stability theory, which guides the updating of the weights of the deep neural network. Likewise, a Lyapunov based algorithm guides the updating of the control signal of the one-step model predictive controller. Simulation results for two cases demonstrate the effectiveness of the proposed control scheme.