We apply memory function formalism to investigate nonequilibrium electron relaxation in graphene. Within the premises of two-temperature model (TTM), explicit expressions of the imaginary part of the memory function or generalized Drude scattering rate (1/τ) are obtained. In the DC limit and in equilibrium case where electron temperature (Te) is equal to phonon temperature (T), we reproduce the known results (i.e., 1/τ T4 when T â‰BG and 1/τ T when T ≫ δBG, where δBG is the Bloch-Grüneisen temperature). We report several new results for 1/τ where TTe relevant in pump-probe spectroscopic experiments. In the finite-frequency regime we find that 1/τ ω2 when ω ωBG, and for ω = ωBG it is ω-independent. These results can be verified in a typical pump-probe experimental setting for graphene.