In this paper, a statistical approximation learning (SAL) method is proposed for a new type of neural networks, simultaneous recurrent networks (SRNs). The SRNs have the capability to approximate non-smooth functions which cannot be approximated by using conventional multi-layer perceptrons (MLPs). However, the most of the learning methods for the SRNs are computationally expensive due to their inherent recursive calculations. To solve this problem, a novel approximation learning method is proposed by using a statistical relation between the time-series of the network outputs and the network configuration parameters. Simulation results show that the proposed method can learn a strongly nonlinear function efficiently.