We have investigated the electronic transport properties of graphene pn junction with spin-orbit coupling. If the incident energy lies between the potentials of the two ends of the pn junction, a particle can penetrate the graphene pn junction by tunneling accompanied by the electron-hole transition. The curve of conductance versus Fermi energy shows steps and reaches its maximum when the Fermi energy lies at the middle of the potentials of the p and n areas. As the length of graphene pn junction increases, the conductance decays exponentially. The spin-orbit coupling leads to a bulk energy gap and edge states; the gap reduces the conductance dramatically and the edge states result in an almost perfect conductance plateau. When the pn region is influenced by randomly doped impurities, the conductance curves are no longer symmetrical in the case of weak doping, while in the strong doping case, the step structures are destroyed but the conductance plateau contributed by the edge states survives well.