Ultra-thin nanopores have become promising biological sensors because of their outstanding signal-to-noise ratio and spatial resolution. Here, we show that boron nitride (BN), which is a new two-dimensional (2D) material similar to graphene, could be utilized for making a nanopore with an atomic thickness. Using an all-atom molecular dynamics simulation, we investigated the dynamics of DNA translocation through the BN nanopore. The results of our simulations demonstrated that it is possible to detect different double-stranded DNA (dsDNA) sequences from the recording of ionic currents through the pore during the DNA translocation. Surprisingly, opposite to results for a graphene nanopore, we found the calculated blockage current for poly(A-T)40 in a BN nanopore to be less than that for poly(G-C)40. Also in contrast with the case of graphene nanopores, dsDNA models moved smoothly and in an unimpeded manner through the BN nanopores in the simulations, suggesting a potential advantage for using BN nanopores to design stall-free sequencing devices. BN nanopores, which display several properties (such as being hydrophilic and non-metallic) that are superior to those of graphene, are thus expected to find applications in the next generation of high-speed and low-cost biological sensors.