We studied a molecular junction with arylalkane self-assembled monolayers sandwiched between two graphene contacts. The arrangement of graphene-based molecular junctions provides a stable device structure with a high yield and allows for extensive transport measurements at 78 K. We observed a temperature-independent current density–voltage (J–V) characteristic and the exponential dependency of the current density on the molecular length, proving that the charge transport occurs by non-resonant tunneling through the molecular barrier. Based on the Simmons model, the bias-voltage dependence of the decay coefficient and barrier height was extracted from variable-length transport characterizations. The J–V data measured were simulated by the Simmons model, which was modified with the barrier lowering induced by the bias voltage. Indeed, there isno need for adjustable fitting parameters. The resulting simulation was in remarkable consistency with experimental measurements over a full bias range up to |V| ≤ 1.5 V for the case of graphene/arylalkane/graphene heterojunctions. Our findings clearly showed the demonstration of stable and reliable molecular junctions with graphene contacts and their intrinsic charge transport characteristics, as well as justifying the application of the voltage-induced barrier lowering approximation to the graphene-based molecular junction.