A Mg-IRMOF-74-III structure with azopyridine molecules attached to its unsaturated metal sites is proposed as a new photoresponsive metal–organic framework (MOF) for $CO_{2}$ capture. Computational simulations indicate that the photochemically induced trans-to-cis transition of the material leads to significant alteration in the $CO_{2}$ capacity. Specifically, the grand canonical Monte Carlo simulation showed a $CO_{2}$ adsorption capacity of 89.6 $cm^{3}/g$ at the trans phase, which is higher than any other photoresponsive MOF reported thus far. Moreover, a large desorption capacity of 82.7 % can be explained from significant alteration of the pore size distribution that comes from the trans-to-cis transition. Our work is anticipated to provide a blueprint for computational designing of the new photoresponsive MOF prior to the actual experimental synthesis.