Abstract: The axial drift of ring laser gyroscopes (RLGs) is a major factor that impacts the performance of the single-axis rotation inertial navigation system. A square support vector machine (SVM) algorithm to forecast the axial RLG drift is proposed in the paper. Latitude and temperature variation during the identification stage are adopted as inputs of model. Employing polynomial, radial basis function (RBF) and wavelet function as the kernel functions, we construct three kinds of support vector machine (SVM), which are SVM, least square support vector machine (LSSVM) and forgetting factor least square support vector machine (FFLSSVM) and compare their capability to forecast the axial RLG drift. The navigational results show that the FFLSSVM method is an effective approach and has the best identification precision. The experimental result of navigation can meet the practical demand.