In this study, new composite materials of montmorillonite, biochar, or aerosil, containing metal–organic frameworks (MOF) were synthesized in situ. Overall, three different MOFs—CuBTC, UTSA-16, and UiO-66-BTEC—were used. Obtained adsorbents were characterized using powder X-ray diffraction, thermogravimetric analysis, nitrogen adsorption porosimetry, scanning electron microscopy, energy-dispersive X-ray spectroscopy, and Fourier transform infrared spectrophotometry. Additionally, the content of metallic and nonmetallic elements was determined to investigate the crystalline structure, surface morphology, thermal stability of the obtained MOF-composites, etc. Cyclic CO₂ adsorption analysis was performed using the thermogravimetric approach, modeling adsorption from flue gasses. In our study, the addition of aerosil to CuBTC (CuBTC-A-15) enhanced the sorbed CO₂ amount by 90.2% and the addition of biochar (CuBTC-BC-5) increased adsorbed the CO₂ amount by 75.5% in comparison to pristine CuBTC obtained in this study. Moreover, the addition of montmorillonite (CuBTC-Mt-15) increased the adsorbed amount of CO₂ by 27%. CuBTC-A-15 and CuBTC-BC-5 are considered to be the most perspective adsorbents, capturing 3.7 mmol/g CO₂ and showing good stability after 20 adsorption-desorption cycles.