In this paper, the impacts of the inverse Stone Thrower Wales (ISTW) defect as an ad-dimer defect on a double gate graphene nanoribbon field effect transistor (DGT) were studied. A DGT structure with a single ISTW defect is firstly analyzed for different positions of the ISTW defect across the width and along the length of the transistor channel. Then the impact of the random distributed ISTW (RDI) defect is investigated and the results indicate the defect density of 0.5% is more favorable due to its relatively better performance in off and on states. Considering how this ad-dimer defect can lead to enhance the transistor performance, a DGT structure including three ISTW defects in specific locations is also investigated which resulted in increasing the on-off current ratio up to 50 and decreasing the sub-threshold swing. The simulation results also show a decrease in ambipolar conduction and attenuation in kink effect. Our simulations has been done based on self-consistent solution of full 3D Poisson and Schrodinger equations within the non-equilibrium Green's function formalism. In the transistor channel, nanoribbons with non-functionalized edges are used.