An artificial neural network provides the possibility to develop molecular potentials with both the efficiency of the classical molecular mechanics and the accuracy of the quantum chemical methods. Here, we develop an ab initio based neural network potential (NN/MM-RESP) to perform molecular dynamics study of zinc ion in liquid water. In this approach, the interaction energy, atomic forces, and atomic charges of zinc ion and water molecules' in the first solvent shell are described by a neural network potential trained with energies and forces generated from density functional calculations. The predicted energies and forces from the NN potential show excellent agreement with the quantum chemistry calculations. Using this approach, we carried out molecular dynamics simulation to study the hydration of zinc ion in water. The experimentally observed zinc-water radial distribution function, as well as the X-ray absorption near edge structure spectrum, is well-reproduced by the MD simulation. Comparison of the results with other theoretical calculations is provided, and important features of the present approach are discussed. The neural network approach used in this study can be applied to construct potentials to study solvation of other metal ions, and its salient features can shed light on the development of more accurate molecular potentials for metal ions in other environments such as proteins.