The effects of magnetization methods with additional permanent magnet on the magnetic field distribution and the levitation force of single domain GdBCO bulk superconductor are investigated with a cubic permanent magnet in their coaxial configuration in zero field cooled state at liquid nitrogen temperature in three different ways. It is found that when the N pole of the cubic permanent magnet, for the levitation force measurement, is placed above the GdBCO bulk superconductor and in the downward direction, the maximal levitation force can be improved to 31.8 N, and that when the N pole of the additional cubic permanent magnet points to upward and sticks to the bottom of the GdBCO bulk, the maximal levitation force is increased up to about 222% of the levitation force of 14.3 N for the system without additional permanent magnet. The maximal levitation force can be improved to 21.6 N (or reduced to 8.6 N), when the GdBCO bulk superconductor is closely placed below and magnetized by the additional cubic permanent magnet with N pole in the upward (or downward) direction, and the additional permanent magnet is removed away after the magnetization, the maximal levitation force is about 151% (or 60%) of 14.3 N for the system without the additional permanent magnet. The results indicate that the levitation force of high temperature bulk superconductors can be effectively improved by introducing additional permanent magnet based on the scientific and reasonable designing of the system configurations, which is very important for the practical design and application of superconducting magnetic levitation system.