Nonlinear spiking neural P (NSNP) systems are one of neural-like membrane computing models, abstracted by nonlinear spiking mechanisms of biological neurons. NSNP systems have a nonlinear structure and can show rich nonlinear dynamics. In this paper, we introduce a variant of NSNP systems, called gated nonlinear spiking neural P systems or GNSNP systems. Based on GNSNP systems, a recurrent-like model is investigated, called GNSNP model. Moreover, exchange rate forecasting tasks are used as the application background to verify its ability. For the purpose, we develop a prediction model based on GNSNP model, called ERF-GNSNP model. In ERF-GNSNP model, the GNSNP model is followed by a “dense” layer, which is used to capture the correlation between different sub-series in multivariate time series. To evaluate the prediction performance, nine groups of exchange rate data sets are utilized to compare the proposed ERF-GNSNP model with 25 baseline prediction models. The comparison results demonstrate the effectiveness of the proposed ERF-GNSNP model for exchange rate forecasting tasks.