Serious startup drift of the Ring Laser Gyroscope (RLG) is observed during cold startup process, which will dramatically degrade the performances of the corresponding Inertial Navigation System (INS). In this paper, correlation analysis method, which analyzes the relationship between the startup drift of the RLG and the temperature change, is used to determine the significant temperature-related terms during gyroscope startup. Based on the significant temperature-related terms and the startup time length, a startup drift compensation model for RLG based on monotonicity-constrained Radial Basis Function (RBF) neural network is proposed and validated. Compared with the raw RLG data without compensation, the standard deviation of the RLG output with the proposed constrained RBF network model is decreased by more than 46%, and the peak-to-peak value is decreased by more than 35%. Compared with the traditional multiple regression model, the standard deviation and peak-to-peak value of the RLG output are decreased by more than 10% and 6%, respectively. Compared with the common RBF network model, the standard deviation and peak-to-peak value of the RLG output are decreased by more than 8% and 3%, respectively. Navigation experiments also validate the effectiveness of the compensation model.