In this article the phonon dispersion and strain effects on the band structure of graphene are investigated using density functional theory. The calculated phonon dispersions ofgraphene show that the LA and TA branches are linear around the Gamam point while the ZA mode shows quadratic energy dispersion. Also, the LO and TO modes at Γ, the LO and LA modes at K, and the ZA and ZO modes at K are doubly degenerate. The electronic band structure of strained graphene maintains the feature of the bands without applying the strain including a pair of two linear dispersive bands crossing at the Fermi level, the Dirac point position and a small asymmetry in the two linear dispersive bands.
