The quantum limit is quite easy to achieve once the band crossing exists exactly at the Fermi level (EF) in topological semimetals. In multilayered Dirac fermion systems, the density of Dirac fermions on the zeroth Landau levels (LLs) increases in proportion to the magnetic field, resulting in intriguing angle- and field-dependent interlayer tunneling conductivity near the quantum limit. BaGa2 is an example of a multilayered Dirac semimetal with its quasi-2D Dirac cone located at EF, providing a good platform to study its interlayer transport properties. In this paper, we report the negative interlayer magnetoresistance induced by the tunneling of Dirac fermions between the zeroth LLs of neighboring Ga layers in BaGa2. When the field deviates from the c-axis, the interlayer resistivity ρzz(θ) increases and finally results in a peak with the applied field perpendicular to the c-axis. These unusual interlayer transport properties are observed together in the Dirac semimetal under ambient pressure and are well explained by the model of tunneling between Dirac fermions in the quantum limit.