Finding an optimal network size is one of the major concerns when building a neural network. In using the local extended Kalman filter (EKF) algorithm, we propose an efficient approach that combines EKF training and pruning as a whole. In particular, the covariance matrix obtained along with the local EKF training can be utilized to indicate the importance of the network weights. As a result, the network size can be determined adaptively to keep pace with the changes in input characteristics. The effectiveness of this algorithm is demonstrated on generalized XOR logic function and handwritten digit recognition.