The distributed activation energy model (DAEM) has been widely used to analyze the thermal decomposition of solid fuels such as lignocellulosic biomass and its components, coal, microalgae, oil shale, waste plastics, and polymer etc. The DAEM with a single distribution of activation energies cannot describe those reactions well since the thermal decomposition normally involves multiple sub-processes of various components. The double DAEM employs a double distribution to represent the activation energies. The Gaussian distribution is usually used to represent the activation energies. However, it is not sufficiently accurate for addressing the activation energies in the initial and final stages of the thermal decomposition reactions of solid fuels. Compared to the Gaussian distribution, the logistic distribution is slightly thicker at the curve tail and suits better to describe the activation energy distribution. In this work, a theoretical analysis of the double logistic DAEM for the thermal decomposition kinetics of solid fuels has been systematically investigated. After the derivation of the double logistic DAEM, its numerical calculation method and the physical meanings of the model parameters have been presented. Three typical types of simulated double logistic DAEM processes have been obtained according to the overlapped situation of two derivative conversion peaks, namely separated, overlapped and partially overlapped processes. It is found that, for the partially overlapped process, the form of the minor peak (overlapped peak or peak shoulder) depends on the values of the frequency factor and heating rate. Considering the simulated processes and related examples from literature, the double logistic DAEM has been remarked as a more reliable tool with abundant flexibility to explain the thermal decomposition of various solid fuels. More accurate results are expected if the double logistic DAEM is coupled with the computational fluid dynamics (CFD) simulation for those reactions mentioned above.