resentation 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.