The cross sections of the processes e(+)e(-)-> K(+)K(-)J/Psi and K(s)(0)K(s)(0)J/Psi are measured via initial state radiation at center-of-mass energies between the threshold and 6.0 GeV using a data sample of 980 fb(-1) collected with the Belle detector on or near the r(nS) resonances, where n=1,2,..5. The cross sections for e(+)e(-)-> K(+)K(-)J/Psi are at a few pb level and the average cross section for K(s)(0)K(s)(0)J/Psi is 1.8 +/- 0.6 (stat)+/- 0.3(syst) pb between 4.4 and 5.2 GeV. All of them are consistent with previously published results with improved precision. A search for resonant structures and associated intermediate states in the cross section of the process e(+)e(-)-> K(+)K(-)J/Psi is performed.