A novel locally polarizable multisite model based on the original cation dummy atom (CDA) model is described for molecular dynamics simulations of ions in condensed phases. Polarization effects are introduced by the electronegativity equalization model (EEM) method where charges on the metal ion and its dummy atoms can respond to the environment. This approach allows us to enhance the original fixed charge CDA model where the charge distribution can adapt to the local solvent structure. To illustrate the new CDApol model, we examined properties of the Zn2+ ion in aqueous solution. Polarizable model and Lennard-Jones parameters were refined for an octahedrally coordinated Zn2+ CDA to reproduce thermodynamic and geometrical properties. Using this locally polarizable model, we were able to obtain the experimental hydration free energy, ion-oxygen distance and coordination number coupled with the standard 12-6 Lennard-Jones model. This model can be used in myriad other applications where local polarization and charge transfer is important.