We theoretically express quantum transport at Dirac points via graphene quantum billiard as a non-magnetic material to connect metallic leads. Our results indicate that the quantum billiard of graphene is similar to a resonant tunneling device. The centerpiece size and the Fermi energy of the graphene quantum billiard play an important role in resonant tunneling. In graphene, a change of carrier density can affect plasmon polaritons. At the Dirac point, the conductivity of graphene depends on the geometry, so that the conduction of the evanescent modes is close to the theoretical value of 4e2/πh (where Planck's constant and the electron charge are denoted by h and e, respectively.). This transport property can be used to justify chaotic quantum systems and ballistic transistors. Our theoretical results demonstrate that the local density of state of the graphene sheet for \({ϵ}_{L}={ϵ}_{R}=0\) is larger than \({ϵ}_{L}={ϵ}_{R}=t\) (where \({ϵ}_{L}\))\({ϵ}_{R}\)( is onsite energy of the left (right) metallic lead) unlike the current obtained from the calculations.