The imaging spectrometer acquires hundreds of contiguous spectral measurements of an area. In many of the applications, the measured data is considered to be linear combinations of constituent materials signatures called endmembers. In practice the number of endmembers are usually much lesser than the total available spectral bands. One of the aims in the unmixing problem is to obtain underlying fractional abundances of every endmember at each location in the acquired scene. It should be noted that at every location, the nature of mixing among the endmembers is governed by the scene-content. It results in nonnegative abundance proportions for each endmember. Due to the presence of noise in the system the problem of unmixing becomes ill-posed. In this paper, we consider the variability in the mixing of endmembers over the acquired scene, for estimating the resultant abundances vectors given the data (measurements) and the endmembers. The relatively coarser instantaneous field of view (IFOV) covered by the hyperspectral imager are unmixed by using the spectral details available at each location in the scene. A Huber-Markov random field (HMRF) is considered across the contiguous spectral space, where a Huber function is defined to incorporate the abundances dependencies within the solution. As the Huber function imposes both the quadratic and the linear penalties, the HMRF preserves the smooth as well as sudden variations in the abundances. The problem is solved by using maximum a posteriori (MAP) estimation by incorporating the HMRF as the prior distribution on the abundances along with the likelihood function. The solution space is restricted to yield physically constrained abundances while optimizing. We conducted experiments on simulated data, constructed with regions having different classes of the mixtures of the endmembers signatures to evaluate the proposed approach. Then the execution is carried out by adding the noise in the data, and the results are compared with the state-of-art approach. Finally, the abundance maps are obtained for the well-known AVIRIS Cuprite mining site. The results validate the effectiveness of the proposed approach.