We investigated temperature-dependent infrared-active phonon modes of honeycomb Li2MnO3 which shows an antiferromagnetic transition at T(N) = 36 K. In the far-infrared frequency region, we observed fourteen phonon modes. We obtained the temperature dependence of each phonon mode from the analysis of optical conductivity spectra by using the Lorentz and the Fano-type oscillator models. We found that the resonance frequencies of nine phonon modes showed an anomalous behavior near T(N) that should be attributed to the spin-phonon coupling. We calculated the magnitude of the spin-phonon coupling constant from the shift in the resonance frequencies of the phonon modes below T(N). Our results suggest that Li2MnO3 is weakly frustrated and that spin-phonon coupling plays a role in antiferromagnetic ordering.