The effective transport of a single-stranded DNA (ssDNA) molecule through a solid-state nanopore is essential to the future success of high-throughput and low-cost DNA sequencing. Compatible with current electric sensing technologies, here, we propose and demonstrate by molecular dynamics simulations the ssDNA transport through a quasi-two-dimensional nanopore in a heterostructure stacked together with different 2D materials, such as graphene and molybdenum disulfide (MoS2). Due to different chemical potentials, U, of DNA bases on different 2D materials, it is energetically favorable for a ssDNA molecule to move from the low-U MoS2 surface to the high-U graphene surface through a nanopore. With the proper attraction between the negatively charged phosphate group in each nucleotide and the positively charged Mo atoms exposed on the pore surface, the ssDNA molecule can be temporarily seized and released thereafter through a thermal activation, that is, a slow and possible nucleotide-by-nucleotide transport. A theoretical formulation is then developed for the free energy of the ssDNA transiting a heterostructure nanopore to properly characterize the non-equilibrium stick-slip-like motion of a ssDNA molecule.