To handle waste gas from nuclear fuel reprocessing, the precise design and preparation of materials exhibiting high-efficiency organic iodide capture performance are still facing huge challenges owing to the severe lack of efficient affinity sites. Herein, we selected an indium-based metal-organic framework, SHF-61, as a precursor and successfully obtained functionalized material, Post-SHF-61, with an azo bond by the diazo coupling reaction between aniline and the amino group of SHF-61. As a result, the conjugation and electron density of the organic component in SHF-61 were significantly enhanced. Static organic iodide adsorption experiments indicated that the CH3I and C2H5I adsorption capacities of 1545 and 848 mg/g for Post-SHF-61 were obviously higher than that of 591 and 271 mg/g for SHF-61 at 75 °C under the same condition. Additionally, the CH3I and C2H5I adsorption mechanisms of SHF-61 and Post-SHF-61 and the possible presence of iodide species in these aforementioned materials were further determined in detail. This study provides some beneficial guides for the development of metal-organic framework-based materials with high organic iodide adsorption capacity.