In this work, the equilibrium adsorption and the kinetic adsorptive breakthrough curve model have been established for CO2 adsorption on K-based sorbent. The equilibrium adsorption of CO2 on the studied K-based sorbent has been developed by several adsorptive equilibrium models to meet the perfect description of the adsorption performance of the K-based sorbent. Then, the kinetic breakthrough curve model is established on the basis of the equilibrium adsorptive model over a fixed bed, whereas the mass balance, the adsorptive equilibrium, and the kinetics of mass transfer with linear driving force (LDF) model have been taken into account to derive the partial differential equations of CO2 adsorption on the K-based sorbent. Moreover, the factors of both molecular diffusion (D-A) and Knudsen diffusion (D-K) have been considered with the internal mass transfer coefficient to describe the internal structure of K-based sorbent. The model results reveal that the kinetic model developed in this work strongly agrees with the experimental results. Consequently, the adsorption equilibrium of the Freundlich isotherm model has been selected, and the parameters of the model have been determined with values of 1.8221/1.6118 and 0.0874/0.1095 for K-L and n, respectively. Furthermore, the analysis for the influence of mass transfer coefficients on the predicted breakthrough curve reveals that the internal mass transfer coefficient is more sensitive than the external mass transfer coefficient.