In real-world situations, a robot may often encounter "under- determined" situation, where there are more sound sources than microphones. This paper presents a speech separation method using a new constraint on the harmonic structure for a simultaneous speech-recognition system in under-determined conditions. The requirements for a speech separation method in a simultaneous speech-recognition system are (1) ability to handle a large number of talkers, and (2) reduction of distortion in acoustic features. Conventional methods use a maximum likelihood estimation in sound source separation, which fulfills requirement (1). Since it is a general approach, the performance is limited when separating speech. This paper presents a two-stage method to improve the separation. The first stage uses maximum likelihood estimation and extracts the harmonic structure, and the second stage exploits the harmonic structure as a new constraint to achieve requirement (2). We carried out an experiment that simulated three simultaneous utterances using impulse responses recorded by two microphones in an anechoic chamber. The experimental results revealed that our method could improve speech recognition correctness by about four points.