Time management is an important component of HLA while Time Advance Mechanism is RTI (Run-Time infrastructure)’s critical technology in implementing time management. One of Time Advance Mechanism is Conservative Time Advance Mechanism. The based premise of Conservative Time Advance Mechanism is that physics system can settle for Realizability and Predictability. But Equipment Maintenance Federate can’t predict the next event time in Maintenance Support Simulation because of infection from other federate. So maintenance support simulation results in deadliness error of RTI. The paper proposes a Federate TimeList method for improves Conservative Event-driven Time Advance Mechanism in HLA. In the end, an example of the maintenance support simulation is particular researched. It is shows that this strategy satisfies the maintenance support simulation effectively.