A technique to determine shear viscosity of Newtonian fluids using molecular dynamics simulation is presented. This technique requires thermostated simulation box and decaying coarse-grain Gaussian velocity profile. The method requires short simulation time as compared to the existing MD methods. Parallel flow of the Newtonian fluids in one direction is analyzed considering velocity profile in two-dimensional Cartesian coordinates. Periodic boundary conditions with the localized velocity profile allow computations in a periodic box with least phonon feedback because of periodicity.