This paper proposes an estimation algorithm to find the moment of inertia, which is essential to design high performance controller for motor drive system. The algorithm finds the moment of inertia observing the position error signal, which contains an error information of moment of inertia, generated by speed observer. Moreover, the proposed algorithm is easily realized in the observer-based speed detection method. The simulation and experimental results are also presented to confirm the performance of moment of inertia estimation method, which shows that the moment of inertia converges to the actual value within several seconds. The speed control responses and the designed speed controller performance match well.