A theoretical investigation is put forward for obtaining effective cross-Kerr nonlinearity of the four-level atom interacting with three electromagnetic fields.Using density-matrix equations and perturbation iterative method,the variation dependence of the third-order susceptibility on the detunings of the applied electromagnetic fields is derived.The results show that a large cross-Kerr nonlinearity can be generated when the detunings of the two weak probe fields are Raman resonant,and the corresponding linear susceptibility and self-Kerr interactions vanish.The realization of the effective Kerr nonlinearity with vanishing absorption is possible in a Raman resonant four-level system.