Cortical neural connectivity has been shown to exhibit a small-world (SW) network topology. However, the role of the topology in neural information processing remains unclear. In this study, we investigated the learning performance of an echo state network (ESN) that includes the SW topology as a reservoir. To elucidate the potential of the SW topology, we limited the numbers of the input and output nodes in the ESN and spatially segregated the output nodes from the input nodes. We tested the ESNs in two benchmark tasks: memory capacity and nonlinear time-series prediction. The SW-ESN exhibited the best learning performance when the spectral radius of the weight matrix was large and when the input and output nodes were segregated. That is, the SW topology provided the ESN with a stable echo state property over a broad range of the weight matrix and efficiently propagated input signals to the output nodes. This result is the same as that of the ESN using a real human cortical connectivity. Thus, the results suggest that the SW topology is essential for maintaining the echo state property, which is the appropriate neural dynamics between input and output brain regions.