This paper presents a Maximum Likelihood approach to multiple fundamental frequency (F0) estimation in each frame of music signals in the frequency domain. The frequencies and amplitudes of the spectral peaks are viewed as observations, and the F0s are viewed as parameters to be estimated. The proposed method considers the potential errors in the peak detection algorithm and treats each peak as “true” and “false” separately. The likelihood models of the “true” and “false” peaks are learned from the monophonic training data, with the assumption that the statistics of the peaks in monophonic and polyphonic signals are similar. The proposed method also incorporates a rectified Bayesian Information Criteria (BIC) to estimate the number of the parameters, i.e. the polyphony. Evaluation is held on randomly mixed chords, which are generated from the previously unseen monophonic tones. Experimental results show the feasibility of this method.