Biped robots require massive power on each leg while walking, hopping, and running. We have developed a flow-based control system - called hydraulic direct drive system - that can achieve high output while avoiding spatial limitations. To implement the proposed system with simple equipment configuration, a pump and single-rod cylinder are connected in a closed loop. However, because compensation for flow rate is impossible in a completely closed loop, owing to the difference in the pressure receiving area caused by the rod, a passive flow compensation valve is employed. This valve has a simple structure and is easy to implement. Further, an additional sensor is required to detect the open/close state because the valve state will cause an error in flow control. Therefore, we implemented a model in the controller to predict the state of the flow compensation valve and formulated a method of switching from flow control to pressure control according to the predicted state. Experimental results indicate that the error of the joint angle is reduced to less than 1.6 degrees for walking patterns, and stable walking is realized when the system is installed in biped humanoid robots.