This paper proposes a matching engine of query-by-singing/humming (QbSH) system which retrieves the most similar music information by comparing the input data with the extracted feature information from polyphonic music like MP3. The feature sequences transcribed from polyphonic music may have many errors. So, to reduce the influence of errors and improve the performance, the chroma-scale representation, compensation and asymmetric DTW (Dynamic Time Warping) are adopted in the matching engine. The performance of various distance metrics are also investigated in this paper. In our experiment, the proposed QbSH system achieves MRR (Mean Reciprocal Rank) of 0.718 for 1000 singing/humming queries when searching from a database of 450 polyphonic musics.