A key challenge for quantum information science is to realize large-scale, precisely controllable, practical systems for multiparty secure communications. Recently, Guidry etal. [Nat. Photonics16, 52 (2022)10.1038/s41566-021-00901-z] have investigated the quantum optics of a Kerr-based optical frequency comb (OFC), which lays out the way for OFC acting as a quantum resource to realize a low-cost and stable multiparty continuous-variable quantum information processing. In this work, we propose a distributed quantum anonymous voting (DQAV) protocol based on discrete modulated coherent states, in which a Kerr-based OFC serves as the resource to generate multi-frequency quantum signals for multiparty voting. We consider both the single-selection and multiple-selection ballot scenarios, and design the phase compensation method for the OFC-based protocol. Voting security is ensured by the basic laws of quantum mechanics, while voting anonymity is achieved by the random assignment of different frequency sources and the homogeneity of the quantum operations taken on the same voting choice. Numerical analysis calculates the secure voting distance over the thermal-lossy channel, showing the advancement of the proposed protocol under multiparty and multivalued voting tasks.