The heat transfer characteristics of China RP-3 aviation kerosene flowing in a vertical downward tube with an inner diameter of 4 mm under supercritical pressures are numerically studied. A ten-species surrogate model is used to calculate the thermophysical properties of kerosene and the re-normalization group (RNG) k-e turbulent model with the enhanced wall treatment is adopted to consider the turbulent effect. The effects of mass flow rate, wall heat flux, inlet temperature, and pressure on heat transfer are investigated. The numerical results show that three types of heat transfer deterioration exist for the aviation kerosene flow. The first type of deterioration occurred at the tube inlet region and is caused by the development of the thermal boundary layer, while the other two types are observed when the inner wall temperature or the bulk fuel temperature approaches the pseudo-critical temperature. The heat transfer coefficient increases with the increasing mass flow rate and the decreasing wall heat flux, while the inlet bulk fluid temperature only influences the starting point of the heat transfer coefficient curve plotted against the bulk fluid temperature. The increase of inlet pressure can effectively eliminate the deterioration due to the small variations of properties near the pseudo-critical point at relatively high pressure. The numerical heat transfer coefficients fit well with the empirical correlations, especially at higher pressures (about 5 MPa).