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In the propulsion system of cryogenic liquid rockets, low-frequency pressure oscillation is a long-standing issue occurring in its feeding pipe, and is not conducive to the normal operation of the rocket. Its mechanism and excitation process are not very clear due to the limitation of the existing numerical method and the difficulty of the real dynamic experiment. Inspired by the periodic suck-back flow phenomenon of steam condensation, the fluctuation of the two-phase interface might be the crucial factor to initiate the low-frequency pressure oscillation. To simulate this interfacial characteristic of cryogenic propellant, a novel numerical model is proposed to predict the mass transfer rate weighted by the interfacial curvature. Aiming at the oxygen jet condensation simulation, the low-frequency pressure oscillation phenomenon is obtained successfully with the excitation frequency of 10.6 Hz, consistent with the natural frequency of the engine test run. It is conducted so the low-frequency pressure oscillation is caused by the periodic condensation of the continuous oxygen vapour plume, along with an oxygen suck-back flow phenomenon. In addition, the results indicate that both the oxygen and liquid oxygen mass flux promote the rise in the frequency of pressure oscillation. These conclusions provide theoretical instructions for the design and operation of the propulsion system of a cryogenic liquid rocket.