Due to the relatively cheap price of diesel, most Marine engines use diesel as Marine fuel, but its emissions contain a lot of carbon. To reduce carbon emissions, International Maritime Organization (IMO) has established an Energy Efficiency Design Index (EEDI) and Energy Efficiency Existing-Ship Index (EEXI). Currently, a popular way is to reduce EEDI by optimizing the heat transfer performance of exhaust gas boilers on new ships, but there is little research on the EEXI index of existing ships. For operating ships, the thermal conductivity of exhaust gas boiler materials and other parameters has been fixed, so the main factors affecting the heat transfer coefficient of the exhaust gas boiler are exhaust gas temperature and flow velocity. Therefore, this paper studies the influence of engine exhaust temperature and flow rate on boiler heat transfer coefficients and optimizes it to achieve the EEXI value required by IMO. Firstly, based on the conservation of mass and energy as the basic equation, a heat exchange model of the exhaust gas boiler is established by using the hybrid modeling method and lumped parameter method. Secondly, for the given boiler, since other parameters are basically unchanged, the input temperature and flow rate of the model are changed by the control variable method, and the temperature of the boiler outlet is simulated by the test algorithm. Through the simulation operation of an Aalborg OC-type boiler, the results show that when the exhaust gas flow velocity is 15 m/s, 17.2 m/s, 22.4 m/s and 25 m/s, respectively, the heat transfer coefficient at each flow velocity increases first and then slowly decreases with the increase of temperature, and there is an optimal temperature at each velocity, which is 230 °C, 227 °C, 225 °C and 224 °C, respectively. The innovation of this study lies in the research on the inlet temperature and flow rate of the exhaust gas boiler of the operating ship based on the EEXI, and the relevant results are obtained, which provides theoretical guidance for the operation management of the exhaust gas boiler of the operating ship.