Carbon capture and storage (CCS) can effectively reduce CO2 emissions from fossil-fuel combustion and mitigate global warming. Among the many CCS technologies, solid-amine based CO2 adsorption exhibits simple operation, great environmental sustainability, and good adsorption performance under post-combustion conditions of humidity, high temperature, and low CO2 partial pressure. Solid amine is always composed of porous solid support and organic amine. However, the disadvantages of complex preparation limit the application of traditional support materials. Therefore, the preparation of a kind of support with convenient synthesis, low cost, and high performance is of great significance for the preparation of solid-amine CO2 adsorbent. In this study, a method for the rapid preparation of an aluminum fumarate metal-organic framework (AlFu) is proposed based on sodium fumarate as the source of the organic ligand and water as the reaction solvent. Post-treatment of AlFu is not required due to the good water solubility of the reactants. The synthesized materials were characterized by X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), Brunauer-Emmett-Teller (BET) nitrogen adsorption/desorption, and thermogravimetric analysis (TGA) techniques. The results show that AlFu can be successfully synthesized at room temperature in 10 min. AlFu shows a typical porous morphology with a specific surface area of 828.44 m2/g. The TGA results show that AlFu is thermally stable up to 400°C. AlFu is a kind of superior solid-amine support material. Polyethylenimine (PEI) was then introduced into the AlFu support by an impregnation method to prepare solid-amine CO2 adsorbent, and the functionalized materials were characterized. The results show that the impregnation method can successfully introduce PEI into the AlFu framework. PEI modification did not destroy the crystal structure, but decreased the XRD characteristic peak intensity of AlFu. Increasing PEI loading leads to the agglomeration of the AlFu skeleton and the decrease of the specific surface area and pore volume of the samples. PEI modification will reduce the thermal stability of the material, but all samples showed good thermal stability below 200°C. Subsequently, the CO2 adsorption performance of the samples was investigated by TGA. The results showed that the optimum PEI content is 50 wt%, and the optimum adsorption temperature of PEI modified AlFu is 75°C, and that the highest CO2 adsorption capacity, 2.68 mmol/g, was obtained under optimum conditions. The CO2 adsorption kinetics onto PEI-AlFu with different PEI loadings was investigated by employing the pseudo-first/second-order kinetic models and fractional-order kinetic model. The results show the fractional-order kinetic model fitted well with the CO2 adsorption experiment data, and that the CO2 adsorption processes of PEI-AlFu were controlled by chemical reaction and physical transmission. Cyclic CO2 adsorption experiments revealed that PEI-AlFu has superior reproducibility after nine CO2 adsorption-desorption cycles. These results suggest that PEI-AlFu has high CO2 adsorption capacity and good reproducibility, and shows great potential for practical CO2 adsorption applications under post-combustion conditions.