The evaluation of the results of geometric error compensation is critical, and it can serve as the feedback of the compensation to help improve the precision of the compensation. In this paper, the closed-loop mode geometric error compensation of five-axis machine tools is presented by correcting the movements of all axes. At first, general geometric error modeling of the machine tool is proposed based on POE theory. The initial positions of linear axes and rotary axes relative to the machine tool are considered and the error twist of each axis containing position-independent errors is established. Second, the closed-loop mode is developed by analyzing the open-loop mode of geometric error compensation. The precision inverse feedback module is formed by introducing the designed tool poses. The output of the feedback is the integrated errors of the revised movements of axes relative to the ideal tool poses of nominal movements of axes. Third, the adaptive correction of movements of axes is proposed based on CSO (chicken swarm optimization). The initializing of the swarm, the Jacobian based moving of roosters, and the moving of chicks containing one mutation are developed. The fitness of the swarm is calculated using the integrated errors relative to the compensation goal in the precision inverse feedback. Finally, simulations by comparing with open-loop mode error compensation and real cutting experiments are proposed on one SmartCNC500_DRTD five-axis machine center to verify the effectiveness of the closed-loop mode geometric error compensation.