Anthracene and carbazole are high-value heavy carbon resources mainly found in the anthracene oil fraction of high-temperature coal tar. Because of their similar structures, traditional solvent crystallization methods are not capable of achieving the separation of high-purity anthracene and carbazole. In this study, MAF-6, a material that can be synthesized in large quantities at room temperature, was used as a sacrificial precursor, carbonized (MC-1000), and subsequently oxidized to form carboxyl-functionalized carbon material (CMC-1000). The presence of carboxyl groups, along with lactones, hydroxyl groups, and carbonyl groups in MC-1000 and CMC-1000, was confirmed through XPS spectra and Boehm titration. CMC-1000 showed an increase of 5.7 mmol/g in oxygen-containing functional groups. The adsorption and separation capacities of MAF-6, MC-1000, and CMC-1000 for anthracene and carbazole in model oil were investigated. FT-IR analysis and DFT calculations demonstrated that the major interaction between CMC-1000 and carbazole involved hydrogen bonding (N–H···O and N–H···N). The results show that CMC-1000 has a high separation selectivity for carbazole over anthracene, with a selectivity of up to 44.4. The formation of hydrogen bonds between the N–H group of carbazole and the oxygen-containing groups on CMC-1000 plays an essential role in achieving high adsorption capacity and selectivity. In addition, CMC-1000 showed strong regenerative capacity, maintaining a selectivity above 29.7 over five cycles.