Selective Laser Melting (SLM) is a powder-based layer-by-layer manufacturing technique to produce metallic customized shape components. The exceptionally high thermal gradient induces residual stress and distorts the part geometry affecting the yield quality. Computational models are instrumental in optimizing the process controls to fabricate high-quality components, and hence several such methods have been explored to simulate the thermal behavior of the process and the heat transfer in the melt-pool. Most of the practiced techniques are computationally expensive, making it infeasible to perform a parametric study. Based on closed-form exact heat conduction solution and Finite Volume Method (FVM), a pseudo-analytical thermal modeling approach has been employed to estimate the melt-pool characteristics and temperature distribution of the SLM process. A moving volumetric Gaussian heat source laser model and Green’s function have been adopted to model the heat input by conduction. The heat loss by conduction and convection has been calculated by implementing Finite Volume discretized equations on a 2-dimensional thin-walled domain with appropriate part boundary conditions. Additionally, the Alternating Direction Implicit iterative technique has been implemented for the fast convergence of the simulation. The model is used to demonstrate the influence of the process parameters and non-linear material phase change for a single-line single layer and multilayer part fabrication. The computed melt-pool dimensions and temperature distribution for varying laser-power, scanning velocity, and layer thickness for Ti6Al4V are validated with the experimental data from the literature with fair agreements.