The change of daily precipitation presents significant non-linear characteristics, and it is very difficult to accurately predict it. In recent years, Long-Short Term Memory (LSTM) has obvious advantages in precipitation prediction. However, the deep structure of LSTM causes its shortcomings such as over-fitting and time lag, which affect the prediction accuracy. Note that the Broad Learning System (BLS) directly calculates weights, and its feature of not requiring multiple iterations can help solve the shortcomings of LSTM. However, noise and outliers still have an adverse effect on modeling. Based on this, an improved Weighted Broad Learning System (WBLS) is proposed. Use a weighted penalty factor to constrain each sample, and assign high and low weights to normal and abnormal samples to increase and decrease their influence. This paper combines the advantages of LSTM and WBLS to propose a LSTM-WBLS daily precipitation prediction model. Empirical research is carried out on the actual data of daily precipitation at Badong Station in Hubei Province in the past 20 years, and factors such as air pressure, temperature, humidity, wind speed and sunshine are taken into consideration. The results show that, compared with the existing prediction models, the LSTM-BLS model has the highest prediction accuracy in all evaluation indicators. In particular, the WBLS module has been added to solve the time lag problem of LSTM. Moreover, under different time steps, the prediction accuracy of the new model also performed best, proving its stability. In terms of computational efficiency, LSTM-WBLS has not decreased compared with LSTM.