The presented work is devoted to the preparation of nanocomposites based on multiwall carbon nanotubes (MWCNTs) and copper (Cu) nanoparticles by a simple chemical method, and to study their sensing properties to hydrogen sulfide (H2S) gas. The Cu decorated multiwall carbon nanotubes (MWCNTs/Cu) were prepared by the deposition of very thin Cu layers on the pristine and functionalized multiwall carbon nanotubes (f-MWCNTs) using both physical (electron beam evaporation (EBE)) and chemical (electrochemical deposition) methods. MWCNTs/Cu prepared in the two above-mentioned ways, their sensing properties were studied, and the results were comparatively analyzed. The effect of the chemical functionalization of MWCNTs by oxygen-containing groups on the sensing properties of these f-MWCNT/Cu nanocomposites has been investigated. All the prepared sensors demonstrated high sensitivity and selectivity to H2S in the air at room temperature. The f-MWCNT/Cu structure obtained by the chemical method demonstrated about 5 times (~400%) higher sensitivity (∆R/R0) to H2S gas compared to the similar structure obtained by the physical method. The temperature effect on sensory characteristics (response and self-recovery time) of the f-MWCNTs/Cu structure was also studied.