The electronic transport properties of monolayer graphene are presented with an Ensemble Monte Carlo method where a rejection technique is used to account for the occupancy of the final states after scattering. Acoustic and optic phonon scatterings are considered for intrinsic graphene and in addition, ionized impurity and surface roughness scatterings are considered for the case of dirty graphene. The effect of screening is considered in the ionized impurity scattering of electrons. The time dependence of drift velocity of carriers is obtained where overshoot and undershoot effects are observed for certain values of applied field and material parameters for intrinsic graphene. The field dependence of drift velocity of carriers showed negative differential resistance and disappeared as acoustic scattering becomes dominant for intrinsic graphene. The variation of electron mobility with temperature is calculated for intrinsic (suspended) and dirty monolayer graphene sheets separately and they are compared. These are also compared with the mobility of two dimensional electrons at an AlGaN/GaN heterostructure. It is observed that interface roughness may become very effective in limiting the mobility of electrons in graphene. (C) 2015 Author(s).