Based on the single particle orbit model and the geomagnetic field dipole model, and considering the relativistic effect, the sixth-order Runge-Kutta algorithm in the Mathematica software is used to numerically calculate and simulate the trajectories of charged particles moving in the magnetic field in the near-Earth region. The generation of auroras is explained, and the approximation of the guiding center of the charged particles moving in the geomagnetic field is discussed. The results show that: (ⅰ) Observed from the earth’s north pole, the protons captured by the earth’s magnetic field drift in the clockwise direction, and the electrons in the anticlockwise direction; (ⅱ) The numerical simulation results of the motion period of each particle motion are in good agreement with the theoretical values in the literature; (ⅲ) When the throwing angle of the incident particle from (4Re,0,0) is less than 7.38°, the charged particle will collide with the atmosphere on the earth’s surface and sink, and there is the possibility of producing auroras. When it is greater than 7.38°, the particles will be bound in the geomagnetic field, forming a radiation belt; (ⅳ) When other conditions are the same, the farther the charged particle throwing point is from the earth, the greater the drift velocity; the greater the throwing angle, the greater the Its drift speed is also greater; (ⅴ) For particles with low energy, the guided center trajectory can well represent the actual trajectory of particles in the first-order approximation.