Bitumen emits a large amount of volatile organic compounds (VOCs) during the production and construction of asphalt mixture, which can cause both environmental hazards and health risks. In this study, a setup was designed to collect the VOCs released by base and crumb rubber-modified bitumen (CRMB) binders and their composition was characterized by thermal desorption-gas chromatography-mass spectrometry (TD-GC-MS). Next, organic montmorillonite (Mt) nanoclay was added into CRMB binder and its inhibiting effect on the VOCs emission of the binder was investigated. Finally, the VOCs emission models for the CRMB and Mt-modified CRMB (Mt-CRMB) binders were established according to reasonable assumptions. The results indicated that the VOCs emission of CRMB binder was 3.2 times larger than that of the base binder. Due to its intercalated structure, the nanoclay can reduce the VOCs emission of CRMB binder by 30.6%. Especially, its inhibition effects on alkanes, olefins, and aromatic hydrocarbons were more significant. After finite element verification, the established model based on the Fick’s second law can describe the emission behavior of CRMB and Mt-CRMB binders well. Overall, the Mt nanoclay can be used as an effective modifier to inhibit the VOCs emission of CRMB binder.