Background: With the constant development and growth of the world’s economy, the demand for energy continues to rise. However, rising oil prices, increasing carbon emissions, and energy shortages will limit economic development and affect living standards. Therefore, further exploitation and utilization of natural gas are of great significance for the sustainable development of national economies and the improvement of civil life. Objective: Natural gas contains acidic gas, such as hydrogen sulfide (H2S), and can lead to physical safety issues, environmental pollution, equipment corrosion, and catalyst poisoning. Therefore, a desulfurization process, which has practical significance, must be carried out to reduce the H2S content to less than 20 mg•m−3. Methods: Currently, the main desulfurization processes involve dry and wet desulfurization methods. The wet desulfurization methods include physical, chemical, and physico-chemical solvent methods, which have a large processing capacity and involve a continuous operation sequence applied to the purification of natural gas containing a high sulfur content. The dry desulfurization methods, which use a solid as the desulfurizer, have high precision, easy operation, and low energy consumption. This method has been widely applied to advanced treatment. : Activated carbon, which has a large surface area, large pore volume, and complex porous structure, is widely used as an adsorbent for desulfurization. When compared with other adsorbents, activated carbon has several advantages, such as a high adsorption capacity and low cost. The H2S removal performance of the adsorbent can be significantly improved after modification. In this study, using a low concentration of H2S and nitrogen to simulate raw fuel gas, cupric nitrate-modified activated carbon was used as the main adsorbent for desulfurization. The effect of the preparation conditions on the H2S removal performance was studied, and the adsorbents were characterized using a series of methods. Results: In this study, a low concentration of H2S and nitrogen were used to simulate raw fuel gas, and cupric nitrate-modified activated carbon was used as an adsorbent. The results from structural analysis indicated a significant change in the surface structure of AC by introducing Cu(NO3)2. Cu(NO3)2 promoted the transformation of micropores into mesopores or macropores and active substances into the pores of AC for desulfurization. The effects of the preparation conditions on the H2S removal performance were studied using a fixed-bed adsorption column. The best preparation conditions for the Cu(NO3)2 modified activated carbon adsorbent involved: a Cu(NO3)2 impregnation concentration of 5%, impregnation time of 24 h, calcination temperature of 300 °C, and calcination time of 2 h. The H2S saturation capacity and desulfurization rate reached 55.4 mg·g−1 and 98.92%, respectively. The H2S saturation capacity was improved by 38.2 mg·g−1 compared with unmodified activated carbon. Conclusion: In this study, a low concentration of H2S and nitrogen were used to simulate raw fuel gas, and cupric nitrate-modified activated carbon was used as an adsorbent. The experimental results showed that the H2S removal performance of the adsorbent was significantly improved using Cu(NO3)2 impregnated activated carbon.