Laser welding process is employed in the manufacturing of critical components where the final assembly units necessitate strict tolerances like low distortions and residual stresses. Laser beam welding offers several advantages like low heat input, very narrow heat affected zone, low residual stresses, low distortions and good mechanical joint properties in the weld joints when compared to the conventional techniques like Tungsten Inert Gas Arc welding processes. However, the implementation of laser beam welding holds certain challenges like process parameters optimization, experimental set-up and handling and expensive costs. In order to minimize the complex experimental process, simulation techniques using Finite Element Methods (FEM) are employed in order to estimate the heat input and weld process optimization prior to the experiments. This greatly helps in the optimization and estimation of the incurred stresses and distortions with the adapted weld process with known input weld process parameters. The present work reports the Gaussian heat source model for the laser welding of Inconel 625 Alloy plates. The developed moving heat source model is presented and demonstrated with the thermal profiles in terms of the thermal histogram, temperature profiles in the joint cross sections through welded region, interface across the joints.