A theoretical investigation is described to study the surface waves on a round liquid jet in a gaseous crossflow, especially Rayleigh-Taylor waves. The linear stability analysis was used to derive the dispersion relation. The acceleration on the liquid jet due to the transverse aerodynamic force was considered in the relation. Results indicate that the hydrodynamic instability is dominated by three terms which are caused by jet velocity, surface tension, and aerodynamic force, respectively. The surface tension contributes to the instability when the wave number is less than unity. Both gas and jet velocities can affect the optimum wavelength and the surface wave growth rate. The critical momentum ratio, at which the contribution of the liquid jet Weber number to the maximum growth rate is as large as that of the cross air Weber number to the maximum growth rate, decreases with the gas Weber number exponentially. If the momentum ratio is less than the critical value, the axial optimum wavelength can be expressed as a power function of gas Weber number. Otherwise, free jet instability theory can be used to study the surface waves on the liquid jet in cross airflow.