The combustion kinetics of corn stalk (CS), paper sludge (PS), and their mixture were studied by thermogravimetric analysis (TGA) using one model-fitting method (Coats–Redfern (CR)) and four model-free methods, namely, Flynn–Wall–Ozawa (FWO), Kissinger–Akahira–Sunose (KAS), Starink, and Friedman methods. TGA experiments were carried out at three different heating rates (10, 20, and 30 °C min−1) and with different weight percentages of PS in the mixture (0%, 20%, 50%, 80%, and 100%). The comprehensive combustion characteristic index decreases with an increase in the weight percentage of PS in the blends and increases with the increasing heating rate. Significant interactions occur in the co-firing of the blends containing 20% and 50% of PS. The co-firing kinetic parameters determined by the CR method show relatively high reliability due to the high correlation coefficient obtained from the linear fitting. The values of average activation energy determined by the model-fitting method are generally lower than those calculated from model-free methods. The co-firing of the blends containing 20% of PS shows the highest comprehensive combustion characteristic index and the lowest average activation energy based on the model-free methods.