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