Effects of additional permanent magnet on the levitation force of a single domain GdBCO bulk superconductor have been investigated with a cylindrical permanent magnet in their coaxial configuration under zero field cooled state at liquid nitrogen temperature. The magnetic polarity N of cylindrical permanent magnet is pointed to the GdBCO bulk superconductor, and the two additional permanent magnet of rectangular parallelepiped shape are fixed on two sides of the GdBCO bulk superconductor in different arrangments. It was found that the levitation force can be improved to about 61.5 N, which is more than 2 times higher than that (29.8 N) of the system without the additional permanent magnet, when the magnetic polarity N of two additional permanent magnets points to the GdBCO bulk superconductor in horizontal direction. The levitation force is reduced to 19.6N, which is about 65.8% of the levitation force 29.8N of the system without the additional permanent magnets, when the magnetic polarity N of two additional permanent magnet are antiparallel to the magnetic polarity N of the cylindrical 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 reasonably designing the system configuration, which is very important during the practical design and applications of superconducting magnetic levitation systems.