Phonons are the main energy carriers for heat conduction in graphene. One of the most important and basic thermal properties is the relaxation time. In this paper, phonon relaxation times are investigated by a normal mode decomposition method to reveal the distinctions of the different phonon modes. The method is based on equilibrium molecular dynamics simulation. In the simulations, the heat current autocorrelation functions are obtained for each single phonon, and the relaxation times are extracted by fitting the functions. In addition, the relations among relaxation time, wave vector, frequency, and temperature are examined. It is found that the variation tendency of the relaxation time with wave vector is close to that of the dispersion with wave vector. For frequency and temperature, they are in agreement with the theoretical model: 1/=nTm. It is shown thatn is 1.56 for acoustic phonons, while for optical phonons, it varies slightly with frequencies; and m is slightly different for each mode. Finally, the contributions of different phonon modes to thermal conductivity are investigated. It is found that low frequency phonons dominate the heat conduction process because of the relatively high relaxation time and density of states.