In this paper, miscible viscous fingering instability in a Darcy and non-Darcy porous media was studied through numerical solution and the formation and growth of finger patterns were discussed. According to the porosity coefficient, the media can be divided into Darcy and non-Darcy categories. Also, flow velocity and fluid used (Newtonian or non-Newtonian) are the factors that limit the use of Darcy’s relation. In this simulation, against most previous studies which had been used the two-phase Darcy’s structural equation to approximate examination of instabilities, a two-dimensional model was used. This model was based on coupling flow equations in porous media (Darcy or Brinkman) and transport of diluted species. The effects of increasing injection rates and viscosity changes were investigated based on Peclet non-dimensional number and viscous ratio on instabilities. Besides, a comparison was done between the results of Darcy’s and Brinkman’s solution at different porosity coefficient and viscosity ratio. Image processing techniques were performed to measure the break through time, perimeter of the interface, fractal dimension and sweep efficiency. With increasing viscosity in Darcy and Brinkman solution, the perimeter of the interface and fractal dimension were increased and more complex fingers generated. As a result, the sweep efficiency of the porous media reduces. In addition, the growth of the media porosity led to sweep efficiency. Finally, it was observed that with increasing injection velocity in Brinkman’s solution, the fingers complexity and perimeter of the interface increased and sweep efficiency decreased.