ZnO–SnO2 branch–stem nanowires were fabricated on a Cu foil using a chemical vapor deposition system through a two-step process. Firstly, SnO2 NWs were synthesized directly on a Cu foil substrate by evaporating SnO powder as a source material. Then, the as-synthesized SnO2 NWs were used as templates for the growth of ZnO–SnO2 branch–stem NWs. The effect of growth time on the growth of the SnO2 NWs on the Cu foil was studied. The gas sensing properties of the SnO2 NW and ZnO–SnO2 branch–stem NW devices were studied using various toxic gases at different temperatures. Both devices exhibited high sensitivity, high selectivity, fast response and recovery times, and stability toward H2S gas. Compared to the pristine SnO2 NW device, the ZnO–SnO2 branch–stem NW device exhibited higher sensitivity and faster response rate toward H2S. Finally, the gas sensing mechanism was also discussed.