A large amount of the waste heat generated during industrial production is not used, which leads to a low energy utilization rate. The recovery of industrial waste heat using heat pumps has the advantages of low energy consumption, high efficiency, safety, and environmental protection. Industrial waste heat has a wide temperature distribution range. Traditional absorption and compression heat pumps can only work in a narrow temperature range due to the thermodynamic cycle, the thermal properties of the working medium, the temperature and pressure resistance of the compressor, and other factors; they cannot simultaneously meet the requirements of a “high heating temperature” and “wide temperature-range heat transfer”. To solve the above problems, this paper proposes a high-temperature heat pump unit based on a coupled cycle of absorption and compression, which can recover low-temperature steam and 50 °C waste heat and produce hot water at 110–130 °C. EES software is used for the mathematical modeling and simulation analysis of the heat pump unit. The results show that, when the driving steam temperature is 140 °C and the waste heat temperature is 50 °C, the heating temperature can reach 110~130 °C and the COP of the system can reach 4.22. Increasing the waste heat outlet temperature and the condensation temperature of the absorption cycle strengthens the COP of the coupled cycle; meanwhile, increasing the evaporation temperature and heating temperature of the absorption cycle reduces the COP of the coupled cycle. The results of this study significantly broaden the operating temperature range and heating temperature of electric heat pumps; our findings therefore have essential research significance for improving energy efficiency in industrial fields.