Music listeners often mishear the lyrics to unfamiliar songs heard from public sources. Speech recognition and acoustic distance can be used to solve this problem. This paper proposes a robust lyric search method for music information retrieval. Firstly, weighted syllable confusion matrix (WSCM) is derived from confusion network. And then, we apply acoustic distance, which is computed based on a WSCM of an automatic speech recognition (ASR) experiment, into dynamic programming (DP) based syllable string matching. The experimental results show that this method increases the hit rate compared with the conventional acoustic distance and edit distance.