Spectroscopic data often suffer from common problems of band overlap and noise. This paper presents a maximum a posteriori (MAP)-based algorithm for the band overlap problem. In the MAP framework, the likelihood probability density function (PDF) is constructed with Gaussian noise assumed, and the prior PDF is constructed with adaptive total variation (ATV) regularization. The split Bregman iteration algorithm is employed to optimize the ATV spectral deconvolution model and accelerate the speed of the spectral deconvolution. The main advantage of this algorithm is that it can obtain peak structure information as well as suppress noise simultaneity. Simulated and real spectra experiments manifest that this algorithm can satisfactorily recover the overlap peaks as well as suppress noise and are robust to the regularization parameter.