This letter presents a detailed study of transport in graphene field-effect transistors (GFETs) with various channel lengths, from 5 μm down to 90 nm, using transferred graphene grown by chemical vapor deposition. An electron-hole asymmetry observed in short-channel devices suggests a strong impact from graphene/metal contacts. In addition, for the first time, we observe a shift of the gate voltage at the Dirac point in graphene devices as a consequence of gate length scaling. The unusual shift of the Dirac point voltage has been identified as one of the signatures of short-channel effects in GFETs.