The study of fluid flow mechanics in fractured porous rocks is crucial in the area of oil and gas production industries, enhanced geothermal system (EGS), CO2 sequestration, disposal of nuclear waste in deep geological repositories (DGR), etc. There are usually two types of flows in fractured rockmass setting. The dominant flow occurs through the fractures whereas there is also a slow movement of fluid through the matrix block. The fluid movement between fracture and matrix is often continuous across the fracture. The present study focuses on the development of a numerical model which can simulate the flow behavior through fracture and matrix simultaneously, which is also known as dual permeability model. To simulate this problem, a 3D model is built in COMSOL Multiphysics 4.3a where a cylindrical geometry is made, and a fracture is defined parallel to the axis of the geometry. The asperity of the fracture is defined by a variable ‘a’ which varies along the x-axis, in such a way that increases the value of ‘a’ alters the geometry of fracture and increases the roughness of fracture. Darcy flow physics is used to simulate the situation with known parameters like porosity, permeability, storage coefficient, etc. Pressure is applied as a boundary condition at two ends of the geometry which acts as driving force for fluid to flow through the block. The influence of fracture asperity on the flow behavior is examined by doing the parametric study and the study shows the decrement in the velocity magnitude with an increase in asperity. The formation of dual flow velocity regime, one along the defined fracture and the other along with the matrix, indicates the efficiency of the developed dual-porosity and permeability model.