This paper presents a novel onset detection algorithm based on cepstral analysis. Instead of considering unnecessary mel-scale or any interests of non-harmonic components, we selectively focus on the changes in particular cepstral coefficients that represent the harmonic structure of an input signal. In comparison with a conventional time-frequency analysis, the advantage of using cepstral coefficients is that it shows the harmonic structure more clearly, and gives a robust detection function even when the envelope of waveform fluctuates or slowly increases. As a detection function, harmonic cepstrum regularity (HCR) is derived by the summation of several harmonic cepstral coefficients, but their frequency indices are defined from the previous frame so as to reflect the temporal changes in the harmonic structure. Experiments show that the proposed algorithm achieves significant improvement in performance over other algorithms, particularly for pitched instruments with soft onsets, such as violin and singing voice.