Rapid and accurate LAI (Leaf Area Index) acquisition is of great significance for remote sensing monitoring of cotton growth, diagnosis of growth stage, extraction of cotton plant area and yield estimation. The present research discussed the characteristics of Sentinel-2 multi-spectral satellite data for remote estimation of cotton LAI. Measured LAI from filed experiments and Sentinel-2 data in 2017 and 2018 were obtained, and LAI estimation model for different and for all growth stages were established basing on single spectral band reflectance on Sentinel-2 and various vegetation index from Sentinel-2 bands. The estimation accuracy of the established LAI models were validated by coefficient of determination (R2), RMSE (root mean square error), mean bias, and slope and intercept, using LOOCV (Leave-One-Out-Cross Validation) method and cross validation, respectively. The results showed that: 1) for the single-band reflectance of sentinel-2 multi-spectral satellite data, two red-edge bands of B6 and B7, and two near-infrared bands of B8 and B8a, were all significantly (P<0.001) correlated to LAI at all three tested growth stages, i.e. bud stage (16-Jun-2017), and flowering stage (23-Jun-2018), and boll stage (2-Aug-2017), with correlation coefficient greater than 0.7. And when the correlation between LAI and band reflectance were performed using data consist of three growth stages, the correlation coefficient for all tested bands reach significant level (P<0.001), and the maximum correlation coefficient was 0.943 of near-infrared narrow band B8a, which center at 865 nm with a wave width of 32 nm. The accuracy of LAI estimation at different development stages was optimized using the near-infrared band B8 which with a central wavelength of 842 nm and a wave width of 145 nm, with all RMSE smaller than 0.465. 2) for seventeen LAI related vegetation indices, including EVI (Enhanced Vegetation Index), MSAVI2 (Modified Soil Adjusted Vegetation Index 2), IRECI (Inverted Red-Edge Chlorophyll Index), etc., most of them were significantly (P<0.001) correlated with LAI, especially atmospheric correction index EVI, soil adjusted index MSAVI2, and red-edge index IRECI, and the coefficient of correlation were over 0.8. EVI provided the best result for LAI estimation at bud stage and boll stage, and at flowering stage it consists by MASVI2, with bud stage RMSE=0.352, and boll stage RMSE=0.367 and flowering stage RMSE=0.323, respectively. 3) LAI estimation models for whole growth stages performed better than these for one single growth stage. And the best LAI estimation models for whole growth period using single spectral band reflectance and vegetation index were respectively obtained by near-infrared narrow band B8a and IRECI, with IRECI performed slightly better, which with R2=0.908 and RMSE=0.425 for LOOCV, and R2=0.951 and RMSE=0.368 for cross validation. Additionally, when apply IRECI-LAI estimation model for whole growth stages on one single growth stage LAI estimation, the accuracy comparison between the IRECI-LAI model and single growth stage LAI models showed that the average cross validation RMSE was only 0.07 greater than the average LOOCV RMSE, indicating the good universality of LAI estimation model for whole growth stages.