We investigate theoretically the behavior of electron spin states near graphene edges at low temperature in the presence of an external electric field. The graphene Hamiltonian is solved directly in the low energy regime including the Rashba spin-orbit interaction. Spin propagation in graphene and spin reflection at the edge are explored by calculating the probability of spin flips between the final and initial states. The spin scattering at the edge is affected by the initial location and the propagating direction of the electron with respect to the edge. Results for an example device structure including the effects of the non-uniform electrostatic field and potential near the graphene edge are presented.