To ensure high-quality electricity, improve the dependability of power systems, reduce carbon emissions, and promote the sustainable development of clean energy, short-term photovoltaic (PV) power prediction is crucial. However, PV power is highly stochastic and volatile, making accurate predictions of PV power very difficult. To address this challenging prediction problem, in this paper, a novel method to predict the short-term PV power using a nonlinear spiking neural P system-based ESN model has been proposed. First, we combine a nonlinear spiking neural P (NSNP) system with a neural-like computational model, enabling it to effectively capture the complex nonlinear trends in PV sequences. Furthermore, an NSNP system featuring a layer is designed. Input weights and NSNP reservoir weights are randomly initialized in the proposed model, while the output weights are trained by the Ridge Regression algorithm, which is motivated by the learning mechanism of echo state networks (ESNs), providing the model with an adaptability to complex nonlinear trends in PV sequences and granting it greater flexibility. Three case studies are conducted on real datasets from Alice Springs, Australia, comparing the proposed model with 11 baseline models. The outcomes of the experiments exhibit that the model performs well in tasks of PV power prediction.