This dissertation focuses on improving the estimation of the peculiar velocity within the Cosmic Microwave Background (CMB) by introducing a novel method based on the Lorentz Lie group and the Newton Method. We We begin with an introduction to the CMB and its mathematical representation using Isotropic Gaussian Random Fields. We then discuss the limitations of the Quadratic Estimator in accurately capturing the effects of peculiar velocity. To address these limitations, we propose a Maximum Likelihood Estimation (MLE) approach that leverages the Lorentz Lie group framework and utilizes the Newton Method to reduce estimation errors. The effectiveness of this new estimator is demonstrated through computer simulations, which show a reduction in Root-Mean-Square Error for peculiar velocity estimation in the CMB. This research contributes to a deeper understanding and more accurate measurement of peculiar velocity within the CMB context.