The recovery of random numbers is one of the key issues for the simulation system to realize the time traceability. The simulation system usually contains a large number of random numbers. In order to restore the system state at any time before, it is necessary to track and record the state evolution of the random number. This kind of tracking and recording work requires a great time and space cost. In order to solve the problem of random number recovery in the simulation system, based on the idea of reversible computation, a reversible linear congruential random number generator is proposed, and the random number generator is realized through the inverse function, general term formula, and inverse distribution function, respectively. It can not only generate random numbers in the forward direction, but also recover the previous random numbers in the reverse direction. The experimental results show that the reversible random number generator is superior to the current general checkpointing implementation in terms of overall space-time performance.