Heaving buoy wave energy converter is applicable to small wave height and short wave period, which are the main characteristics of the China Sea. The device captures the wave power by buoy's heaving motion, transfers it by hydraulic system, and converts it into the electric power by generator. Power Take-Off (PTO) of the device is related to the resistance of the hydraulic system. However, effects of the hydraulic damping on the motion of buoy are often neglected and the study on the optimal hydraulic system is rare. In this paper, a new theoretical analysis has been developed, which is more applicable to the buoy considering hydraulic system. The paper establishes the governing equation considering buoyancy, wave dynamic force and hydraulic damping. The displacement and the velocity of the buoy are both obtained. The time-averaged power captured is calculated by integrating the square-velocity expression derived, and the existence of the maximum PTO is proved. Theoretical result is compared with the experimental result. The paper demonstrates the displacements and average output power of the buoy with different values of damping and inertia coefficients. The results of the study could be a guidance for the PTO design of the heaving buoy sets. (C) 2015 Elsevier Ltd. All rights reserved.