K+K- production in two-photon collisions has been studied using a large data sample of 67 fb-1 accumulated with the Belle detector at the KEKB asymmetric e+e- collider. We have measured the cross section for the process γγ → K +K- for center-of-mass energies between 1.4 and 2.4 GeV, and found three new resonant structures in the energy region between 1.6 and 2. 4 GeV. The angular differential cross sections have also been measured.