In this paper, we consider the approximate identification problem for hidden Markov models, i.e. given a finite- valued output string generated by an unknown hidden Markov model, find an approximation of the underlying model. We propose a two-step procedure for the approximate identification problem. In the first step the underlying state sequence corresponding to the output sequence is estimated directly from the output data. In the second step the system matrices are calculated from the obtained state sequence and the given output sequence. In a simulation example the performance of our proposed method is compared with the performance of the classical Baum-Welch approach for identification of hidden Markov models.