In this paper, we consider a new background elimination method for Raman spectra. As a background is usually slowly varying with respect to wavelength, it could be approximated by a slowly varying curve. However, the usual curve-fitting method cannot be applied because there is a constraint that the estimated background must be beneath a measured spectrum. To meet the requirement, we adopt a polynomial as an approximating function and show that background estimation could be converted to a linear programming problem which is a special case of constrained optimization. In addition, we present an order selection algorithm for automatic baseline elimination. According to the experimental results, it is shown that the proposed method could be successfully applied to experimental Raman spectra as well as synthetic spectra. Copyright © 2011 John Wiley & Sons, Ltd.