Cryogenic liquid fuel launch vehicles encounter longitudinal unstable vibrations during flight, which is a serious threat to the normal operation of rockets. Such vibrations exhibit typical low-frequency characteristics and often occur during the jet condensation of cryogenic liquid oxygen in propellant pipelines. To solve this problem at the source, the characteristics of the jet condensation oscillation and flow pattern transition must be investigated. Based on the height function method, a modified mass transfer model was used to dynamically capture the interfacial curvature. The relationship between the condensation pulsation frequency and two-phase interfacial curvature was established, and the frequency of the pressure oscillation was found to be 9.8-10.6 Hz. The results indicated that three typical types of jet condensation oscillations exist: stable pulsation, gas plume oscillation, and suck-back flow. The pressure amplitude of the suck-back and oscillation flows was up to 130 kPa, whereas that of the stable pulsation was only 1-3 kPa. From the dimensional analysis, the transition threshold of the flow pattern was Jc^*=7.3 when dimensionless structure parameter L^*=2.2. When Jc^*>7.3, a suck-back oscillating flow pattern appeared. The dimensionless criterion could precisely predict the condensation flow pattern. This provides a theoretical basis and technical support for the design of cryogenic liquid fuel rockets.