Abstract: Based on the auxiliary differential equation (ADE) finite-difference time-domain (FDTD) method, distributions of electromagnetic fields and Lorentz force densities in a dispersive chiral column are simulated. Firstly, relationships between electromagnetic polarization densities and induced electromagnetic polarization densities, as well as coupled electromagnetic polarization densities of chiral media, are presented based on the constitutive relations. Wave equations and recurrence formula of electric are given. Secondly, the Lorentz force density in chiral media containing bound electric charge and electric current densities, as well as bound magnetic charge and magnetic current densities, is derived. Then, we verify the correctness of the ADE-FDTD method and the Lorentz force density method by comparing with literature's results. Finally, distributions of fields and optical forces for an active chiral cylinder are simulated. The contribution of electromagnetic current and electromagnetic charge densities to the Lorentz force density is discussed. The work in this paper provides some theoretical guidance for chiral media's potential engineering applications in optical tweezers and measurement of chiral parameter.