Au/Ni ohmic contact to p-type P-doped ZnO (P:ZnO) is succeeded and investigated. The specific contact resistance rho(c) decreases with increasing annealing temperature up to 300 degrees C, but increases beyond that. After annealing at 300 degrees C, rho(c) is 0.0052 cm(2), a decrease by about 15 times from 0.076 cm(2) of the as-deposited contact. The sheet resistance R-s of p-type P:ZnO monotonously increases with the annealing temperature. The mechanisms causing the rho(c) and R-s variation with the annealing temperature are studied. During thermal annealing in vacuum (2x10(-5) mbar), competitions exist between Zn out-diffusion and Ni and Au diffusion into ZnO. Zn out-diffusion can improve the ohmic contact performance by producing more acceptors or surface states in the interfacial layer, while Ni and Au diffusion into ZnO can kill the acceptors or surface states in the interfacial layer.