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A band-to-band tunneling field-effect transistor (FET) can achieve a subthreshold slope steeper than 60 mV/dec at room temperature, but the on-current is low due to existence of the tunneling barrier. Graphene has a monolayer-thin body which is amenable to strain. By using self-consistent quantum transport simulations, we show that with local strain applied at the tunneling junction between the source and the channel in a graphene nanoribbon tunneling FET, the on-current can be significantly improved by over a factor of 10 with the same off-current, no matter at the ballistic limit or in the presence of inelastic phonon scattering.