Human-robot interaction through music in real environments is essential for robots, because such a robot makes people enjoyable. To deal with real music signals by using robot's own ears, we propose a beat-tracking algorithm for a robot based on semi-blind independent component analysis (SB-ICA) and spectro-temporal pattern matching (STPM). SB-ICA suppresses a self-generating sound such as singing or scatting which heavily affects beat-tracking due to its periodicity. STPM provides quick adaptation to beat changes because it is able to use a shorter matching window than conventional beat-tracking methods based on self-correlation functions. We thus developed a music robot which steps, sings, and scats according to musical beats based on the proposed beat-tracking method. The experimental results using the music robot showed highly noise-robust beat-tracking even when the robot was singing or scatting, and quick adaptation to beat changes like a human clapping sound whose tempo is always changing.