Graphene is an interesting material with a number of desirable electrical properties. Graphene-based negative differential resistance (NDR) devices hold great potential for enabling the implementation of several elements required in electronic circuits and systems. In this article we propose a novel device structure that exhibits NDR using single layer graphene that is able to be fabricated using standard lithography techniques. Using theoretical simulation, we show that graphene nanoribbon (GNR) junctions exhibit NDR effect if a gap is introduced in the structure in the transport direction of the ribbon. Using standard lithography techniques, we produce a GNR and use electro-migration to create a nanogap by breaking the GNR device. Scanning electron microscopy images show the formation of a tunnel gap. The predicted NDR phenomenon is experimentally verified in the current-voltage characteristic of the device. The linear and non-linear characteristics of the I-V responses before and after breakdown confirm that the NDR effect arises from the tunnel gap.