  The tunneling of electrons and holes in quantum structures plays a crucial
role in studying the transport properties of materials and the related devices.
8-Pmmn borophene is a new two-dimensional Dirac material, which hosts tilted
Dirac cone and chiral, anisotropic massless Dirac fermions. We develop the
transfer matrix method to investigate the Klein tunneling of massless fermions
across the smooth NP junctions and NPN junctions of 8-Pmmn borophene. Like the
sharp NP junctions of 8-Pmmn borophene, the tilted Dirac cones induce the
oblique Klein tunneling. The angle of perfect transmission to the normal
incidence is 20.4 degrees, a constant determined by the Hamiltonian of 8-Pmmn
borophene. For the NPN junction, there are branches of the Klein tunneling in
the phase diagram. We find that the asymmetric Klein tunneling is induced by
the chirality and anisotropy of the carriers. Furthermore, we show the
oscillation of electrical resistance related to the Klein tunneling in the NPN
junctions. One may analyze the pattern of electrical resistance and verify the
existence of asymmetric Klein tunneling experimentally.
