Graphene is an emerging nanomaterial believed to be a potential candidate for post-Si nanoelectronics, due to its exotic properties. Recently, a new graphene nanoribbon crossbar (xGNR) device was proposed which exhibits negative differential resistance (NDR). In this paper, a multi-state memory design is presented that can store multiple bits in a single cell enabled by this xGNR device, called Graphene Nanoribbon Tunneling Random Access Memory (GNTRAM). An approach to increase the number of bits per cell is explored alternative to physical scaling to overcome CMOS SRAM limitations.