In the context of the Sustainable Development Goals (SDGs), the prediction of green financial returns is of great significance for optimizing resource allocation and promoting environmental sustainability. In this paper, ARIMA model is used to capture the linear trend and seasonal characteristics of time series; then Particle Swarm Optimization (PSO) algorithm is introduced to optimize the parameters of LSTM model, and finally ARIMA-PSO-LSTM combination model is constructed to forecast the results of green finance investment returns. The experimental results show that the PSO algorithm can further improve the prediction ability of the LSTM neural network model, and the combination of the ARIMA model and the PSO-LSTM model into a new ARIMA-PSO-LSTM prediction model can retain the advantages of the two and improve the prediction performance. The simulation experiments found that the prediction errors (RMSE and MAPE values) of the ARIMA-PSO-LSTM model were reduced by 90.98%, 83.1%, 69.73%, and 54.06% compared with the ARIMA model and the PSO-LSTM model, respectively, and it is obvious that the ARIMA-PSO-LSTM model is better in predicting the return of green financial investment.