Abstract: Raman spectroscopic data often suffers from common problems of bands overlapping and random Gaussian noise. Spectral resolution can be improved by mathematically removing the effect of the instrument response function. In this paper, a novel method to deconvolute the degraded spectrum with the Laplacian-Markov priori was proposed, solving by split Bregman optimization scheme, which was fast, robust to noise and easy to implement. The Laplacian-Markov priori was proposed to save the shape peaks and suppress the noise. A data weighted operator was introduced to spectral deconvolution to find a balance between band narrowing and noise suppression. The method could estimate spectral structural details as well as suppress the noise effectively. Experimental results with real Raman spectra manifest that this algorithm can deconvolute the overlapping peaks as well as suppress the noise effectively. Owing to the fast of computing time, it is expected that the proposed method has considerable value in practice.