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In view of the problem that most remote sensing prediction methods take spectral information as the main feature of the model and ignore the temporal variation characteristics when obtaining leaf area index (LAI) quickly and accurately, the UAV was equipped with a five channel multispectral camera to obtain the multispectral images of different growth periods of maize in the study area. The vegetation indices of maize in corresponding growth period were calculated based on the images. Then the sub models of each growth period were established by using the vegetation indices. The contribution of the root mean square error (RMSE) of each sub model to the RMSE of the whole growth period model was calculated based on Shapley theory. The weight of each sub model was given based on its contribution. The combination estimation model was built with LAI timeseries variation characteristics according to the weight. And different combination models were built based on support vector regression (SVR) algorithm, multilayer perceptron (MLP), random forest (RF) algorithm and XGBoost algorithm for comparison. The results showed that the estimation effect of the combined LAI estimation model based on Shapley theory was better than that of the whole growth period LAI estimation model. Compared with other LAI estimation models (SVR-Shapley, MLP-Shapley and RF-Shapley), the XGBoost-Shapley model had the best estimation effect (R2 was 0.97, RMSE was 0.021, RPD was 6.9). Thus the XGBoost-Shapley model was applied to LAI prediction in the study area. The research results showed that the LAI change rate in different growth periods were different, and the prediction results accorded with the growth trend of maize in different growth periods. The research result can provide a method for remote sensing monitoring of field maize growth.