The hydrogen evolution reaction (HER) is a critical step in water splitting and demands efficient and low-cost catalysts for real applications. Pt catalyzes HER efficiently, however, its scarcity and high cost inspire researchers to explore metallic catalysts with core-shell nanostructures. Precise tailoring of Pt catalysts at atomic monolayer level would shed insights on the relationship between electronic structure and electrocatalytic properties. Herein, we report the preparation of Au-Pt core-shell nanoparticles deposited on graphene sheets with tunable Pt monolayer coverage by controlling Cu underpotential deposition (UPD)-Galvanic replacement cycles. The electrochemical results suggest that Au-Pt with monolayer Pt shows superior electrocatalytic activity toward HER. Increasing the thickness of Pt shell results in the decrease of the electrocatalytic activity, which might be attributed to the decreased electronic interactions of Au core with outmost surface Pt atoms as confirmed by X-ray photoelectron spectroscopic characterization. The present research would offer a design criterion for metallic nanostructures in realizing catalysts with high performance.