Devices in which a single strand of DNA is threaded through a nanopore could be used to efficiently sequence DNA(1-9). However, various issues will have to be resolved to make this approach practical, including controlling the DNA translocation rate, suppressing stochastic nucleobase motions, and resolving the signal overlap between different nucleobases(4,7). Here, we demonstrate theoretically the feasibility of DNA sequencing using a fluidic nanochannel functionalized with a graphene nanoribbon. This approach involves deciphering the changes that occur in the conductance of the nanoribbon(10,11) as a result of its interactions with the nucleobases via pi-pi stacking(12,13). We show that as a DNA strand passes through the nanochannel(14), the distinct conductance characteristics of the nanoribbon(15-17) (calculated using a method based on density functional theory coupled to non-equilibrium Green function theory(18-20)) allow the different nucleobases to be distinguished using a data-mining technique and a two-dimensional transient autocorrelation analysis. This fast and reliable DNA sequencing device should be experimentally feasible in the near future.