Considering　the　anharmonic　vibrations　and　the　interactions　between　electron　and　phonon　of　atoms,　in　this　article　we　study　the　temperature　dependence　of　Grüneisen　parameter,　thermal　expansion　coefficient　at　low　temperature　and　phonon　relaxation　time　by　using　the　theory　and　method　of　solid　state　physics.　The　influences　of　the　anharmonic　vibration　of　the　atom　on　the　above　parameters　are　further　discussed.　The　obtained　results　are　as　follows.　1)　The　thermal　expansion　coefficient　of　graphene　is　a　negative　value　when　the　temperature　drops　below　room　temperature.　The　absolute　value　of　the　thermal　expansion　coefficient　of　graphene　increases　monotonically　with　the　increase　of　temperature.　The　thermal　expansion　coefficient　of　graphene　is　-3.64　×　10-6　K-1　at　room　temperature.　2)　The　value　of　Grüneisen　parameter　is　zero　in　the　harmonic　approximation.　If　the　anharmonic　vibration　is　considered,　the　Grüneisen　parameter　will　increase　slowly　with　the　increase　of　temperature.　Its　value　is　between　1.40　and1.42　and　the　change　is　almost　linear.　And　we　find　that　the　influence　of　the　second　anharmonic　term　is　less　than　that　of　the　first　anharmonic　term　on　Grüneisen　parameter.　3)　The　phonon　relaxation　time　decreases　with　the　increase　of　temperature.　The　rate　changes　rapidly　at　low　temperature　(T　©　2017　Chinese　Physical　Society.