  Aiming to understand the main spin relaxation mechanism in graphene, we
investigate the spin relaxation with random Rashba field induced by both
adatoms and substrate, by means of the kinetic spin Bloch equation approach.
The charged adatoms on one hand enhance the Rashba spin-orbit coupling locally
and on the other hand serve as Coulomb potential scatterers. Both effects
contribute to spin relaxation limited by the D'yakonov-Perel' mechanism. In
addition, the random Rashba field also causes spin relaxation by spin-flip
scattering, manifesting itself as an Elliott-Yafet--like mechanism. Both
mechanisms are sensitive to the correlation length of the random Rashba field,
which may be affected by the environmental parameters such as electron density
and temperature. By fitting and comparing the experiments from the Groningen
group [J\'ozsa {\it et al.}, Phys. Rev. B {\bf 80}, 241403(R) (2009)] and
Riverside group [Pi {\it et al.}, Phys. Rev. Lett. {\bf 104}, 187201 (2010);
Han and Kawakami, {\it ibid.} {\bf 107}, 047207 (2011)] which show either
D'yakonov-Perel'-- (with the spin relaxation rate being inversely proportional
to the momentum scattering rate) or Elliott-Yafet--like (with the spin
relaxation rate being proportional to the momentum scattering rate) properties,
we suggest that the D'yakonov-Perel' mechanism dominates the spin relaxation in
graphene. The latest experimental finding of a nonmonotonic dependence of spin
relaxation time on diffusion coefficient by Jo {\it et al.} [Phys. Rev. B {\bf
84}, 075453 (2011)] is also well reproduced by our model.
