Based on a representation of a stochastic integral of Ornstein–Uhlenbeck (O–U) type, the exact simulation algorithm of the tempered stable O–U process is given in this paper. The algorithm employs the double rejection method and the general acceptance–rejection technique. The time complexity of the double rejection method is uniformly bounded over all values of the parameter. And the acceptance probability of the acceptance–rejection technique can be improved to as close to 1 as possible. Thus, the implementation of the algorithm is efficient. The performance of the simulation method is evidenced by some empirical results.