The cooling of a injector effects on the vapor pressure of cryogenic oxidizer spray, and it decides the phase transition point at the ignition process, when the combustion chamber pressure increases drastically. The phase transition of oxidizer spray affects the ignition characteristics, and several ignition tests with the LOx/$GCH_4$ uni-element coaxial swirl injector was performed in the different initial temperatures of oxidizer injector, in order to investigate the effect of injector cooling on the ignition transient characteristics. At the transition point of oxidizer phase, where the combustion chamber pressure increased over the LOx vapor pressure, the temporary quenching phenomenon of the flame occurred. The lower temperature of chilled down injector and tubing tends to move up the phase transition earlier.