A new metal–organic framework (MOF), Co2(L)2(azpy)n (compound 1, H2L = 5-(pyridin-4-ylmethoxy)-isophthalic acid, azpy = 4,4′-azopyridine), was synthesized by a solvothermal method and further characterized by elemental analysis, IR spectra, thermogravimetric analysis, single-crystal and powder X-ray diffraction. The X-ray single-crystal diffraction analysis for compound 1 indicated that two cis L22− ligands connected to two cobalt atoms resulted in a macrocycle structure. Through a series of adsorption tests, we found that compound 1 exhibited a high capacity of CO2, and the adsorption capacity could reach 30.04 cm3/g. More interestingly, under 273 K conditions, the adsorption of CO2 was 41.33 cm3/g. In addition, when the Co-MOF was irradiated by a 730 nm laser, rapid temperature increases for compound 1 were observed (temperature variation in 169 s: 26.6 °C), showing an obvious photothermal conversion performance. The photothermal conversion efficiency reached 20.3%, which might be due to the fact that the parallel arrangement of azo units inhibited non-radiative transition and promoted photothermal conversion. The study provides an efficient strategy for designing MOFs for the adsorption of CO2 and with good photothermal conversion performance.