A low resistance Ohmic contact to p-type GaN is essential for reliable operation of electronic and optoelectronic devices. Such contacts have been made using Ni/Au and Pd / Au contacts to p-type Mg-doped GaN (1.41×1017 cm−3) grown by metalorganic chemical vapor deposition ( MOCVD ) on ( 0001 ) sapphire substrates. Thermal evaporation was used for the deposition of those metals followed by annealing at temperatures of 400 ∼ 700 °C in an oxygen and nitrogen mixed gas ambient, then subsequently cooled in liquid nitrogen which reduced the specific contact resistance from the range of 9.46∼2.80×10−2 Ωcm2 to 9.84∼2.65×10−4 Ωcm2 for Ni/Au and from the range of 8.35∼5.01×10−4 Ωcm2 to 3.34∼1.80×10−4 Ωcm2 for Pd/Au. The electrical characteristics for the contacts were examined by the current versus voltage curves and the specific contact resistance was determined by use of the circular transmission line method (c-TLM). The effects of the cryogenic process on improving Ohmic behavior (I-V linearity) and reducing the specific contact resistance will be discussed from a microstructural analysis which reveals the metallurgy of Ohmic contact formation.