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The effects of uniaxial strain on the bandgap and performance of a top gate graphene nanoribbon (GNR) on insulator transistor are studied using pi-orbital basis 3-D ballistic quantum simulation. The bandgap variation with strain shows zigzag pattern for the three families of nanoribbon. The variation is linear between two turning points and has almost equal magnitude of gradient for all the families. The ON-state and the off-state currents reduce and the ON/OFF current ratio increases with the type of strain that results in larger bandgap. The variation of off current and ON/OFF current ratio is exponential, and that of on current is linear with strain and is independent of the type of strain applied. The intrinsic switching delay reduces and the intrinsic cutoff frequency increases with the type of strain that results in smaller bandgap. While the off -state current and the on/off current ratio improve with strain, the on-state current and switching performance degrade, and vice versa. Therefore, careful tradeoff should be considered in strain engineering of GNR transistors.