High leakage current, low ON/OFF current ratio, and ambipolar behavior are important problems which can limit the application of graphene nanoribbon field effect transistors in digital circuits. In this paper, a novel structure with symmetric pocket doping in channel region (SPD-GNRFET) is proposed to lower destructive effects of band to band tunneling (BTBT) in GNRFETs and improve their performance. Two pockets of n-type doping are applied to both sides of channel at the channel to drain and source regions with similar n-type impurity.These pockets modulate the potential profile at both sides of channel and enlarges the straight distance along the GNR between conduction and valance bands at drain/source to channel junction. For demonstrating the superiority of the proposed structure over its conventional counterpart, wide ranges of channel length, SPD region length, and SPD region impurity are investigated. Our simulations reveal the proper potential of the SPD structure for digital applications. Also, symmetric device structure and use of same n-type doping for pockets, drain, and source regions are other advantages of SPD structure in comparisons with its similar structures from device performance and fabrication points of view.