A novel algorithm based on Kalman filtering is developed for the learning of a layered neural network. The problem of adjusting the weight can be regarded as that of estimating a signal state vector of a linear process. The proposed algorithm, though computationally complex, has an adaptively varying learning rate, while the back-propagation algorithm has constant learning rate. Some experiments conducted for XOR and auto-associative image compression problems have shown that the proposed learning algorithm usually converges in a few iterations and the error is comparable to that of the well-known back-propagation algorithm.