Graphene-based vertical heterostructures, particularly stacks incorporated with other layered materials, are promising for nanoelectronics. The stacking of two model Dirac materials, graphene and topological insulator, can considerably enlarge the family of van der Waals heterostructures. Despite good understanding of the two individual materials, the electron transport properties of a combined vertical heterojunction are still unknown. Here, we show the experimental realization of a vertical heterojunction between Bi2Se3 nanoplate and monolayer graphene. At low temperatures, the electron transport through the vertical heterojunction is dominated by the tunneling process, which can be effectively tuned by gate voltage to alter the density of states near the Fermi surface. In the presence of a magnetic field, quantum oscillations are observed due to the quantized Landau levels in both graphene and the two-dimensional surface states of Bi2Se3. Furthermore, we observe an exotic gate-tunable tunneling resistance under high magnetic field, which displays resistance maxima when the underlying graphene becomes a quantum Hall insulator.