The Kibble balance is a device for realization of the mass unit, kilogram, in the new international system of units. A Kibble balance requires a magnet system to supply the magnetic flux that precisely links the electrical power and mechanical power. Therefore, the magnet system is one of the core elements in Kibble measurement, and its performance can significantly affect the final mass measurement accuracy. This paper analyzes how the magnet system affects the Kibble balance uncertainty and reviews the performance of various Kibble balance magnet systems. The comparison of different magnet systems shows that the BIPM magnet design has merits in efficiency of magnetic field generation, magnetic shielding and geometrical symmetry, which can be considered as one of the best Kibble balance magnet designs.