The laser ablation plasma thruster is a novel electric propulsion thruster, which combined the laser ablation and electromagnetic acceleration. In order to investigate the plasma expansion and ionization in the laser ablation plasma thruster, which was difficult to obtain from experiments, the 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 plasma properties, taking into account ionization, plasma absorption and shielding. The ablation plasma velocity, temperature and electron number density were predicted by using the numerical method. The calculated results showed that the peak values of ablation plasma velocity, temperature and electron number density fraction were distributed at the front of the plasma plume. Moreover, the discharge characteristics and thrust performance were tested with different charged energy, structural parameters and propellants. The thrust performance was proven to be improved by electromagnetic acceleration.