In this study, a high-performance H2S sensor that operates at RT was successfully fabricated using biodegradable electroactive polymer-polyurethane-urea (PUU) and PUU-activated-carbon (AC) composites as sensitive material. The PUU was synthesized through the copolymerization of biodegradable polycaprolactone diol and an electroactive amine-capped aniline trimer. AC, with a large surface area of 1620 m2/g and a pore diameter of 2 nm, was derived from coconut-shell waste. The composites, labeled PUU-AC1 and PUU-AC3, were prepared using a physical mixing method. The H2S-gas-sensing performance of PUU-AC0, PUU-AC1, and PUU-AC3 was evaluated. It was found that the PUU sensor demonstrated good H2S-sensing performance, with a sensitivity of 0.1269 ppm−1 H2S. The H2S-gas-sensing results indicated that the PUU-AC composites showed a higher response, compared with PUU-AC0. The enhanced H2S-response of the PUU-AC composites was speculated to be due to the high surface-area and abounding reaction-sites, which accelerated gas diffusion and adsorption and electron transfer. When detecting trace levels of H2S gas at 20 ppm, the sensitivity of the sensors based on PUU-AC1 and PUU-AC3 increased significantly. An observed 1.66 and 2.42 times’ enhancement, respectively, in the sensors’ sensitivity was evident, compared with PUU-AC0 alone. Moreover, the as-prepared sensors exhibited significantly high selectivity toward H2S, with minimal to almost negligible responses toward other gases, such as SO2, NO2, NH3, CO, and CO2.