In order to investigate the influence of magnetic field on quantum dynamics of a three-level trapped ion, the Jaynes-Cummings model of a single three-level trapped ion in magneto-optical field is solved exactly. The mean vibrational quantum number of the trapped ions and squeezing effect of ion vibrational state are numerically analyzed. Results show that time evolution of the mean vibrational quantum number displays the collapse-revival characteristics which is similar to those in two-level Jaynes-Cummings model, and the stronger the magnetic field is, the longer the revival period will be. In the case of strong magnetic field coupling, the magnetic field can significantly enhance squeezing effect of ion vibration state. The maximum amplitude squeezing can be observed when the ions are initially excited in the superposition state.