Speech act classification is an essential part of a dialogue system because it is very important to catch user's intention. The previous approaches on speech act classification were focused on obtaining high performances in a single-domain, but they did not deal with a feature interference problem that frequently rises in a multi-domain. In this paper, we propose a two-step system for speech act classification in a multi-domain. In a first step, the proposed system detects a dialogue domain associated with user's utterance. In the second step, the proposed system determines the speech act of his/her utterance based on the statistical information of the detected domain. Owing to this architecture, the proposed system showed higher precision of 5.5% than the baseline system based on the mixed statistical information.