This report describes an algorithm for the accelerated computation of the convolution of a Lorentz line shape (pressure broadened) with spectral line data. A computational savings of approximately 10 has been achieved over conventional methods. The Lorentz function has been decomposed into three functions, each of which is convolved independently at optional sampling intervals. Criteria for the determination of the sampling interval of the Lorentz function for a resultant error of 0.1 percent is described. The report contains a listing of the computer program based on the algorithm and sample results in the spectral region 3550 to 3650/cm due to water and carbon dioxide.