Given the limited operating ability of a single robotic arm, dual-arm collaborative operations have become increasingly prominent. Compared with the electrically driven dual-arm manipulator, due to the unknown heavy load, difficulty in measuring contact forces, and control complexity during the closed-chain object transportation task, the hydraulic dual-arm manipulator (HDM) faces more difficulty in accurately tracking the desired motion trajectory, which may cause object deformation or even breakage. To overcome this problem, a compliance motion control method is proposed in this paper for the HDM. The mass parameter of the unknown object is obtained by using an adaptive method based on velocity error. Due to the difficulty in obtaining the actual internal force of the object, the pressure signal from the pressure sensor of the hydraulic system is used to estimate the contact force at the end-effector (EE) of two hydraulic manipulators (HMs). Further, the estimated contact force is used to calculate the actual internal force on the object. Then, a compliance motion controller is designed for HDM closed-chain collaboration. The position and internal force errors of the object are reduced by the feedback of the position, velocity, and internal force errors of the object to achieve the effect of the compliance motion of the HDM, i.e., to reduce the motion error and internal force of the object. The required velocity and force at the EE of the two HMs, including the position and internal force errors of the object, are inputted into separate position controllers. In addition, the position controllers of the two individual HMs are designed to enable precise motion control by using the virtual decomposition control method. Finally, comparative experiments are carried out on a hydraulic dual-arm test bench. The proposed method is validated by the experimental results, which demonstrate improved object position accuracy and reduced internal force.