The popular Long Short-Term Memory (LSTM) based precipitation prediction models suffer from overfitting and time lag. Broad Learning System (BLS), which does not require multiple iterations, helps to solve the above disadvantages of LSTM. Weighted Broad Learning System (WBLS) reduces the impact of noise and outliers on precipitation prediction accuracy by introducing a weighted penalty factor constraint to assign sample weights in the BLS. Thus, a LSTM-WBLS daily precipitation prediction model is proposed in this paper. The daily precipitation at Badong station in Hubei province is selected for empirical study. And the influence of air pressure, temperature, humidity, wind speed and sunshine on precipitation is considered. The experimental results demonstrate that the LSTM-BLS model has significantly improved the prediction accuracy in the evaluation indexes of RMSE, MAE and R2 compared with existing prediction models. The prediction accuracy of the new model outperforms existing models at different time steps, proving its stability. In particular, the direct calculation of weights by WBLS does not make any reduction in operational efficiency of LSTM-WBLS.