In collider experiments, such as KEKB, crab crossing method is a promising way to increase the luminosity. We are planning to apply crab crossing to laser-Compton scattering (LCS), a collision of electron beam and laser, to achieve a higher luminosity leading to a higher flux X-ray source. It is well known that the collision angle affects the luminosity. It is the best when the collision angle is zero, head-on collision, for a higher luminosity but difficult to construct such system especially when using an optical cavity for laser. Concerning this difficulty, we are planning crab crossing by tilting the electron beam using an rf-deflector. Although crab crossing in LCS has been already proposed , nowhere has demonstrated yet. We are going to demonstrate and conduct experimental study with our compact accelerator system in Waseda University. In this conference, we will report mainly about expected results of crab crossing LCS.