We　propose　a　general　approach　to　speed　up　quantum　adiabatic　processes　for　fast　quantum　information　transfer　in　a　three-level　system.　In　the　approach,　by　using　an　intermediate　Hamiltonian　which　is　assumed　to　be　formed　by　the　original　Hamiltonian　H-0(t)　and　its　counterdiabatic　driving　Hamiltonian　H-cd(t)　with　a　simple　linear　relationship,　we　design　exact　dynamics　following　the　eigenstates　of　the　intermediate　Hamiltonian　to　speed　up　the　desired　population　processes.　We　apply　the　present　approach　to　a　three-level　system　to　show　that　by　suitably　choosing　the　parameters,　not　only　the　population　processes　could　be　sped　up,　but　also　the　existence　of　the　undesired　off-diagonal　terms,　the　populations　of　the　intermediate　states,　and　even　the　shapes　of　the　pulses　would　be　controllable　in　the　speeding　up　scheme.