The laser ablation plasma thruster is a novel electric propulsion thruster, which combined the laser ablation and electromagnetic acceleration. In order to investigate the plume expansion and ionization in the laser ablation plasma thruster which was difficult to obtain from experiments, the two-dimensional heat conduction model and fluid dynamics model were established. The heat conduction model was established to calculate the target ablation, taking into account temperature dependent material properties, phase transition, dielectric transition and phase explosion. The fluid dynamics model was used to calculate the plume properties, taking into account ionization, plume absorption and shielding. The good agreement between calculated and experimental data validated our model, while the plume velocity, temperature and electron number density were predicted by using the numerical method. The calculated results showed that the plume uniformly expanded into the ambience with a mushroom shape, and the peak values of plume velocity, temperature and electron number density fraction were distributed at the front of the plume. The ceramic tube limited the radial expansion of the plume, and enhanced the velocity, temperature and ionization degree nearby the wall, due to the interaction between the plume and the wall. Otherwise, the effects of laser fluence on plume properties and thrust performance of the thruster were investigated utilizing the numerical model.