A novel scheme is proposed to investigate the possible giant Kerr nonlinearity in a crystal of molecular magnets. The crystal is subjected to one dc magnetic field and two probe and coupling ac magnetic fields. By studying the steady-state behavior of the medium, we show that an enhanced Kerr nonlinearity with negligible absorption can be achieved under condition of slow light levels, just by properly adjusting the coupling field. Also, the transient evolution of nonlinear dispersion is proposed. It is found that the frequency detunings of probe and coupling fields, as well as the intensity of coupling field, lead to the large Kerr nonlinearity. Our results can be used as a guideline for optimizing and controlling the switching process in the crystal of molecular magnets, which is much more practical than that in the atomic system because of its flexible design and the long relaxation times.