This paper proposes a matching engine for a query-by-singing/humming (QbSH) system with polyphonic music files like MP3 files. The pitch sequences extracted from polyphonic recordings may be distorted. So we use chroma-scale representation, pre-processing, compensation, and asymmetric dynamic time warping to reduce the influence of the distortions. From the experiment with 28 hour music DB, the performance of our QbSH system based on polyphonic database is very promising in comparison with the published QbSH system based on monophonic database. It shows 0.725 in MRR(Mean Reciprocal Rank). Our matching engine can be used for the QbSH system based on MIDI DB also and that performance was verified by MIREX 2011.