We performed three-dimensional unsteady calculations of reactive flows, based on the compressible N-S equation, to investigate the hydrodynamic instability of premixed flames under the low temperature environment. As the unburned-gas temperature became lower, the growth rate decreased and the unstable range narrowed. This was due mainly to the reduction of the burning velocity of a planar flame. The normalized growth rate increased with a decrease of the unburned-gas temperature. This was because that the thermal-expansion effects became stronger owing to the increase of the temperature ratio of burned and unburned gases. In addition, we compared with the results of asymptotic analysis and confirmed that both results were almost the same at sufficiently small wave numbers.