This research develops a gravity compensation method that determines the mass of a task object easily and compensates for the external force caused by the task object when it is conveyed by a hydraulic teleoperation construction robot. Moreover, this study establishes a master-slave system for this robot; two joysticks act as the master, and an excavator with four links (fork glove, swing, boom, and arm) represents the slave. To compensate for the influence of gravity, a previous gravity compensation method is proposed and applied to the boom and arm. However, it is ineffective during the conveyance process especially when the task object is heavy because the driving force is influenced by gravity of the task object. Therefore, this research presents a gravity compensation method that can effectively determine the mass of a grasped object and compensate for the external force induced by its gravity, as verified through pressing, grasping, and conveying experiments.