Neural networks are frequently employed to model species distribution through backpropagation methods, known as backpropagation neural networks (BPNN). However, the complex structure of BPNN introduces parameter settings challenges, such as the determination of connection weights, which can affect the accuracy of model simulation. In this paper, we integrated the Grey Wolf Optimizer (GWO) algorithm, renowned for its excellent global search capacity and rapid convergence, to enhance the performance of BPNN. Then we obtained a novel hybrid algorithm, the Grey Wolf Optimizer algorithm optimized backpropagation neural networks algorithm (GNNA), designed for predicting species' potential distribution. We also compared the GNNA with four prevalent species distribution models (SDMs), namely the generalized boosting model (GBM), generalized linear model (GLM), maximum entropy (MaxEnt), and random forest (RF). These models were evaluated using three evaluation metrics: the area under the receiver operating characteristic curve, Cohen's kappa, and the true skill statistic, across 23 varied species. Additionally, we examined the predictive accuracy concerning spatial distribution. The results showed that the predictive performance of GNNA was significantly improved compared to BPNN, was significantly better than that of GLM and GBM, and was even comparable to that of MaxEnt and RF in predicting species distributions with small sample sizes. Furthermore, the GNNA demonstrates exceptional powers in forecasting the potential non-native distribution of invasive plant species.