Even though ratio of air to fuel is the major factor in determining the thermal efficiency of a boiler, how to optimize the ratio in the real operation is still more like art than science, especially for a gas/solid multi-fuel combustion system. This study, taking operation data from a real gas/solid fuels co-firing boiler, is aimed to develop the thermal efficiency model. To cope with the complexity of combustion mechanism in a co-firing boiler, this study proposed a two-tier approach to modeling thermal efficiency. The first tier is to transform the plant input variables into the derived variables, which are physically and statistically meaningful to the model-building. In the second tier, this study proposed an adaptive modeling approach by employing nonnegative garrote variable selection and auto-regression integrated moving average correction. Both approaches are first time proposed in building the thermal efficiency model for boilers. The prediction error of boiler thermal efficiency made by the acquired model reaches less than 0.03%. The high accuracy of the proposed modeling approaches makes the implementation of the model-based control of ratio of air to fuel for improving boiler's efficiency readily practicable. (C) 2013 Elsevier Ltd. All rights reserved.