Abstarct: Thermal Viscous Fingering Instability is one the different kinds of instabilities in Porous medium, which occurs at the common interface of two fluids, differing in viscosity and temperature. In this study, the instability is discussed in a Porous media. The main goal of the present work is studying the viscous dissipation influence on Thermal Viscous Fingering Instability. In the following, the mass and thermal peclet number influence on concentration and thermal front and Thermal Viscous Fingering Instability in a Porous medium with anisotropic properties are reviewed. In this study, in order to demonstrate the viscosity’s dependency on concentration and temperature, two parameters and are used which represent solutal mobility ratio and thermal mobility ratio, respectively. Other engaged parameters are Lewis number, thermal lag coefficient and Brinkman number. In non-linear simulation section, using COMSOL software, this instability is simulated during different time intervals and different fingering growth mechanism are studied at two concentration and temperature fronts. Also, a study in average temperature and width density curves, mixing length, sweep efficiency is delivered, helping us understand the concept of this instability much more. Results show that viscosity dissipation with increasing temperature will decrease fluid viscousity, this reduction is more aggressive in moving fluid with higher viscosity, therefore mobility ratio and instability growth rate will decrease. As a result, flow becomes more laminar, while mixing length decreases and sweeping efficiency increases. Examining peclet number influence demonstrate that with decreasing peclet number, which results in higher penetration potency, two fluids will have expanded boundary area and are distributed more in one another, resulting in fingerings reach the front’s end later and a more laminar flow. Thermal Viscous Fingering Instability in a medium with n Anisotropic Properties Simulation results indicate that while medium and mass’s Permeability increases in flow direction than Permeability in the Perpendicular direction to flow, instability will decrease and a more laminar flow will be gained.