In this paper, we study the application of an HMM (hidden Markov model) to the problem of representing protein sequences by a stochastic motif. A stochastic protein motif represents the small segments of protein sequences that have a certain function or structure. The stochastic motif, represented by an HMM, has conditional probabilities to deal with the stochastic nature of the motif. This HMM directly reflects the characteristics of the motif, such as a protein periodical structure or grouping. In order to obtain the optimal HMM, we developed the "ilerative duplication method" for HMM topology learning. It starts from a small fully-connected network and iterates the network generation and parameter optimization until it achieves sufficient discrimination accuracy. Using this method, we obtained an HMM for a leucine zipper motif. Compared to the accuracy of a symbolic pattern representation with accuracy of 14.8 percent, an HMM achieved 79.3 percent in prediction. Additionally, the method can obtain an HMM for various types of zinc finger motifs, and it might separate the mixed data. We demonstrated that this approach is applicable to the validation of the protein database; a constructed HMM has indicated that one protein sequence annotated as "leucine-zipper like sequence" in the database is quite different from other leucine-zipper sequences in terms of likelihood, and we found this discrimination is plausible.