This paper studied the sloshing stability of a liquid-filled cylindrical tank subjected to longitudinal excitation. A pendulum model is used to obtain equivalent dynamics Mathieu equation of the liquid sloshing under the longitudinal excitation. Based on the perturbation method, the stability boundaries are then obtained with the variation of the damping, liquid height and diameter of the tank. The results show that the damping, the liquid height and the diameter of tank have an important effect on stability boundaries.