A natural gradient algorithm with an adaptive learning rate for blind source separation is proposed.The adaptive learning rate only depends on the negative exponential of the square sum of the kurtosis of neural networks outputs.The initial convergence speed is very fast because of large learning rate (according to small kurtosis).After an initial period

the learning rate decreases slowly due to large kurtosis

giving rise to small steady-state errors.Simulation with under-Gaussian as sources and in the instantaneous mixing case shows that the proposed algorithm has faster convergence and smaller steady-state error than those without adaptive learning rate.