  The transport properties of electrons in graphene $p$-$n$ junction with
uniform Kekul\'e lattice distortion have been studied using the tight-binding
model and the Landauer-B\"uttiker formalism combined with the nonequilibrium
Green's function method. In the Kekul\'e-ordered graphene, the original $K$ and
$K^{\prime}$ valleys of the pristine graphene are folded together due to the
$\sqrt{3} \times \sqrt{3}$ enlargement of the primitive cell. When the valley
coupling breaks the chiral symmetry, special transport properties of Dirac
electrons exist in the Kekul\'e lattice. In the O-shaped Kekul\'e graphene
$p$-$n$ junction, Klein tunneling is suppressed, and only resonance tunneling
occurs. In the Y-shaped Kekul\'e graphene $p$-$n$ junction, the transport of
electrons is dominated by Klein tunneling. When the on-site energy modification
is introduced into the Y-shaped Kekul\'e structure, both Klein tunneling and
resonance tunneling occur, and the electron tunneling is enhanced. In the
presence of a strong magnetic field, the conductance of O-shaped and on-site
energy-modified Y-shaped Kekul\'e graphene $p$-$n$ junctions is non-zero due to
the occurrence of resonance tunneling. It is also found that the disorder can
enhance conductance, with conductance plateaus forming in the appropriate range
of disorder strength. The ideal plateau value is found only in the Kekul\'e-Y
system.
