Non-negative matrix factorization (NMF) is widely used for music transcription because of its efficiency. However, the conventional NMF-based music transcription algorithm often causes harmonic confusion errors or time split-up errors, because the NMF decomposes the time-frequency data according to the activated frequency in its time. To solve these problems, we proposed an NMF with temporal continuity and harmonicity constraints. The temporal continuity constraint prevented the time split-up of the continuous time components, and the harmonicity constraint helped to bind the fundamental with harmonic frequencies by reducing the additional octave errors. The transcription performance of the proposed algorithm was compared with that of the conventional algorithms, which showed that the proposed method helped to reduce additional false errors and increased the overall transcription performance.