We investigate charge transport in a chemically reduced graphene oxide (RGO) film of sub-micron thickness. The I-V curve of RGO film shows current switching of the order of ∼10(5) above the threshold voltage. We found that the observed I-V curve is consistent with quantum tunnelling based charge transport. The quantum tunnelling based Simmons generalized theory was used to interpret the charge transport mechanism which shows that the current switching phenomenon is associated with transition from direct to Fowler-Nordheim (F-N) tunneling. The absence of current switching in the I-V curve after stripping away the oxygen functional groups from chemically RGO film confirms that the presence of these groups and reduced interaction between adjacent layers of RGO play a key role in charge transport. Such metal-based current switching devices may find applications in graphene-based electronic devices such as high voltage resistive switching devices.