In this study, a general nonlinear mathematical model on torsional pendulum vibration was built, aiming to reduce the error of traditional model for measuring the moment of inertia for large scaled plate-like objects. The average value method under the weak nonlinear condition proposed by VanderPol was adopted to achieve the linear equation of torsional pendulum vibration and derive the new mathematical expression of the torsional pendulum vibration for measuring the moment of inertia. The results achieved with the new model showed higher repeatability and accuracy in the measurement of the moment of inertia.