Nitrous oxide is a suitable propellant for rocket engines and has been widely used in various countries, given its high saturated vapor pressure, which enables self-pressurization. Because nitrous oxide is in a state of vapor–liquid equilibrium in tanks, it is easy to form a gas–liquid two-phase flow by cavitation in feed line. Since accurately estimating the performance of rocket engines requires evaluating the characteristics of propellant flows, tests reported in this paper were conducted using hybrid rocket engines under three conditions: cold flow test, hot firing test at low back pressure, and hot firing test at high back pressure. With consideration to the subcooling degrees, nitrous oxide may be in an unsteady superheated state in the upstream flow of the injector. In a comparison of the pressure ratios between the injector in each test condition, it is observed that a critical two-phase flow was formed in the injector in the cold flow test and in the low backpressure firing test. In the high backpressure hot firing test, the injector flow may be choked, but the large oscillations were observed in chamber pressure and thrust. According to the FFT analysis results, these oscillations were caused by chugging and acoustic oscillation. In light of these experimental results, it is suggested that when the chamber pressure fluctuates due to combustion instability such as chugging and acoustic oscillation, it may affect the injector flow characteristics and the critical two-phase flow.