We investigated the carrier transport in multi-layer MoS2 in consideration of contact resistance (Rc) and interlayer resistance (Rint). Bottom graphene contact was suggested to overcome the degradation of Id modulation in back gated multi-layer MoS2 field effect transistor (FET) due to the accumulated Rint and increased Rc with thickness increasing. As a result, non-degraded drain current (Id) modulation with flake thickness increasing was achieved due to the non-cumulative Rint. Benefited from the low Rc brought by the negligible Schottky barrier at graphene/MoS2 interface, intrinsic carrier transport properties immune to Rc was investigated in multi-layer MoS2 FET. ~ 2 times enhanced carrier mobility was attained from the self-screened channel in the bottom graphene contacted device, compared to those with top metal contacts.