The rapid, accurate estimation of leaf nitrogen content (LNC) and plant nitrogen content (PNC) in cotton in a non-destructive way is of great significance to the nutrient management of cotton fields. The RGB images of cotton fields in Shihezi (China) were obtained by using a low-cost unmanned aerial vehicle (UAV) with a visible-light digital camera. Combined with the data of LNC and PNC in different growth stages, the correlation between N content and visible light vegetation indices (VIs) was analyzed, and then the Random Forest (RF), Support Vector Machine (SVM), Back Propagation Neural Network (BP), and stepwise multiple linear regression (SMLR) were used to develop N content estimation models at different growth stages. The accuracy of the estimation model was assessed by coefficient of determination (R2), root mean squared error (RMSE), and relative root mean square error (rRMSE), so as to determine the optimal estimated growth stage and the best model. The results showed that the correlation between VIs and LNC was stronger than that between PNC, and the estimation accuracy of different models decreased continuously with the development of growth stages, with higher estimation accuracy in the peak squaring stage. Among the four algorithms, the best accuracy (R2 = 0.9001, RMSE = 1.2309, rRMSE = 2.46% for model establishment, and R2 = 0.8782, RMSE = 1.3877, rRMSE = 2.82% for model validation) was obtained when applying RF at the peak squaring stage. The LNC model for whole growth stages could be used in the later growth stage due to its higher accuracy. The results of this study showed that there is a potential for using an affordable and non-destructive UAV-based digital system to produce predicted LNC content maps that are representative of the current field nitrogen status.