A new scheme to estimate the moment of inertia in the servo motor drive system in very low speed is proposed in this paper. The speed estimation scheme in most servo drive systems for low-speed operation is sensitive to the variation of machine parameter, especially the moment of inertia. To estimate the motor inertia value, the observer using the Radial Basis Function Network (RBFN) is applied. A control law for stabilizing the system and adaptive laws for updating both of the weights in the RBFN and a bounding constant are established so that the whole closed-loop system is stable in the sense of Lyapunov. The effectiveness of the proposed inertia estimation is verified by simulations and experiments.