The vibrational energy relaxation rate of an excited C-H stretching mode on the hydrogen-terminated H/C(111)1X1 surface is calculated using Bloch-Redfield theory combined with classical molecular dynamics. The lifetime of an excited state is determined by the strength of the power spectrum of the force on the stretching mode at the resonance frequency. The lifetime of the first excited state is found to the 60 ps at 300 K which is shorter than the Si-H stretching mode lifetime on the H/Si(111)1X1 surface. The lifetime of the v=2 first overtone state is found to be 200 times shorter (0.30 ps). Analysis of the power spectrum of the fluctuating force along the C-H bond suggests that the mechanism of the energy relaxation for the v=1 stretching state on the H/C(111)1X1 surface is due to lower-order interactions than on the H/Si(111)1X1 surface. The predicted fast relaxation of the overtone state may cast some doubt on the observability of that state.