Hall thruster is a kind of plasma optics device, which is used mainly in space propulsion. To study the influence of magnetic field on the performance of a 5 kW hall thruster, a two-dimensional PIC-MCC model was built. The Bohm diffusion was modeled by using a Brownian motion instead of the Bohm collision method and the near-wall conduction was modeled by a secondary electron emission model. When the mass flow rate is 5 mg/s, the thruster performance like thrust, efficiency and discharge current was simulated under a discharge voltage from 300 to 1,000 voltage. At first, the performance under constant magnetic field was simulated. The results showed that the magnetic field could not restrain the electrons as the discharge voltage increased. Later, the performance under varied magnetic field was simulated. The results showed that increasing the magnetic field strength with the increasing discharge voltage could restrain the electrons more efficiently, which proved that increasing the magnetic field strength is necessary for high specific impulse operation of hall thruster. At last, the performance measurement experiment of the thruster was carried out, and the experimental results verified the accuracy of the simulation results.