An analysis/synthesis technique based on harmonic sinusoidal modeling of speech is used to develop a new hidden Markov model (HMM) based speech enhancement algorithm. State sequence estimation is done using a standard HMM-based approach. State-based enhancement is carried out by assuming a harmonic model for speech, i.e., by representing each block of speech as a sum of sine waves in terms of a set of amplitudes, phases, and harmonically related frequencies. Given the maximum a-posteriori probability (MAP) state sequence, the amplitudes, phases, voicing, and fundamental frequency are estimated. Simulation results are presented, comparing the performance of the proposed algorithm to that of a standard HMM-based approach. The proposed method was found to reduce the structured residual noise normally associated with HMM-based algorithms.