We describe the results of computer simulations of the dynamical behavior of a neural network model based on BP learning incorporated with stochastic resonance (SR Neural Network). This model is effective in solving the XOR problem, as reported in our previous work. This network is a small-scale network for practical engineering. In this study, therefore we apply four bits parity problem and investigate learning abilities in the enhanced network to establish our SR method. From the results of experiments, we see the learning abilities of our network are improve more than the limited abilities of the traditional BP learning network. We also observe the stochastic resonance in our network.