The stability of learning rate in neural network identifiers and controllers is one of the challenging issues which attracts great interest from researchers of neural networks. This paper suggests adaptive gradient descent algorithm with stable learning laws for modified dynamic neural network (MDNN) and studies the stability of this algorithm. Also, stable learning algorithm for parameters of MDNN is proposed. By proposed method, some constraints are obtained for learning rate. Lyapunov stability theory is applied to study the stability of the proposed algorithm. The Lyapunov stability theory is guaranteed the stability of the learning algorithm. In the proposed method, the learning rate can be calculated online and will provide an adaptive learning rare for the MDNN structure. Simulation results are given to validate the results.