The radiative transfer equation (RTE) describes the sounder observed radiance as a result of contribution from various surface properties, atmospheric temperature, and absorbing gas profiles. Retrieval of these geophysical parameters from the sounder data requires an inverse solution to the RTE problem. In the presence of noise in observation data, the maximum likelihood method is often used to find the most probable solution from an ensemble described by a probability density function. In recent years, general purpose graphics processing units with hundreds of computing cores have become more affordable for scientific computation. This work will explore the use of GPU in speedup of the maximum likelihood solution to the ill-posed retrieval problem. For the infrared atmospheric sounding interferometer high-resolution sounder having 8641 channels, the use of GPU on maximum likelihood estimation shows a promising speedup of compared to a single-threaded native CPU version.