A hydraulic system is disclosed that has first and second passages connecting a pump to an actuator in closed-loop manner, and first and second load-holding valves within the first and second passages. The hydraulic system may also have a regeneration valve connected to the first and second passages between the actuator and the first and second load-holding valves to selectively connect the first and second passages. The hydraulic system may further have a controller configured to cause a control valve to simultaneous move the first and second load-holding valves toward flow-blocking positions when pump displacement is about zero. The controller may also be configured to selectively cause the regeneration valve to connect the first and second passages when pump displacement is non-zero, and to cause only one of the first and second load-holding valves to move to its flow-blocking position when the regeneration valve connects the first and second passages.