We examine spectral subtraction with both amplitude and phase spectra for improved speech enhancement performance by the method of maximum a posterior. Spectral subtraction is a very valid and direct denoising algorithm, but it has a vital problem, i.e., it may generate 'musical noise'. An adaptive harmonic model is utilized. Maximum a posterior is considered to derive the phase estimator, which is extra applied to amplitude spectral subtraction. Different from others, the extra parameters in our algorithm are considered as random variables, and the main extra parameters are amplitude and phase. The phase of the speech signal is assumed to have von Mises circular distribution, and the amplitude is to have normal distribution. The assumptions are applied to Bayesian theory, and we derived the update formulae of the parameters of the speech model, that is, phase estimator and amplitude estimator. Thus, we obtained the phase and amplitude of each harmonic. Simulation results show the further improvement of spectral subtraction.