A polymer membrane-coated palladium (Pd) nanoparticle (NP)/single-layer graphene (SLG) hybrid sensor was fabricated for highly sensitive hydrogen gas (H2) sensing with gas selectivity. Pd NPs were deposited on SLG via the galvanic displacement reaction between graphene-buffered copper (Cu) and Pd ion. During the galvanic displacement reaction, graphene was used as a buffer layer, which transports electrons from Cu for Pd to nucleate on the SLG surface. The deposited Pd NPs on the SLG surface were well-distributed with high uniformity and low defects. The Pd NP/SLG hybrid was then coated with polymer membrane layer for the selective filtration of H2. Owing to the selective H2 filtration effect of the polymer membrane layer, the sensor had no responses to methane, carbon monoxide, or nitrogen dioxide gas. On the contrary, the PMMA/Pd NP/SLG hybrid sensor exhibited a good response to exposure to 2% H2: on average, 66.37% response within 1.81 min and recovery within 5.52 min. In addition, reliable and repeatable sensing behaviors were obtained when the sensor was exposed to different H2 concentrations ranging from 0.025 to 2%.