In this paper the finite element method is used to calculate the transient temperature field distribution during hydrogen pump chill-down in a liquid rocket engine before the engine starts. The chill-down flow rate and chill-down time are both related to the consumption of liquid hydrogen. If the chill-down flow rate or time is not adequate, it may produce a deleterious effect on the engine start reliability. If an excessive amount of liquid hydrogen is consumed, the payload is diminished. Therefore, effectively controlling chill-down time (or chill-down flow rate) is of great engineering value. This paper establishes a two-dimensional axial symmetry mathematical model; the results calculated using the model fitting well with the experimental data. It is shown that the chill-down time under current engineering conditions could possibly be reduced.