This paper investigates the prediction of spectrum usage by wireless local area networks based on recurrent nerural networks (RNNs). The prediction results can be used to enhance the spectrum efficiency in dynamic spectrum sharing, and accuracy of spectrum sensing in cognitive radio networks. Observed time series of duty cycle (DC), which indicates the spectrum usage trend, is utilized to predict the future DC by the RNN. At first, we reveal a drawback of prediction by a single RNN, and this approach is denoted by a conventional approach in this paper. Specifically, the prediction results may have a significant biased error if the observed DCs are biased to either high or low values. For this problem, we propose the DC prediction, which employs two RNNs for high and low DC cases, respectively. The prediction algorithm at first identifies the state of current DC either high or low. Then, the RNN for the identified state is selected for an accurate DC prediction. Numerical evaluations based on comprehensive measurement experiments of spectrum usage have presented that the proposed DC prediction can improve the accuracy of DC prediction compared to the conventional approach.