The perturbative theory of laser induced collisional charge exchange (LICCE) is presented, in which the laser induced collisional charge exchange is described as a four body system and the compound atomic and ionic states are used as basis states of LICCE, and the equation of motion for the probability amplitudes of the states are obtained. The numerical results of LICCE in Ca + Sr are obtained for the first time through numerical calculation, and the comparison between the theoretical results and the experimental one (obtained by W. R. Green et al.) confirms the interpretation of the peaks at 477.0 nm as due to LICCE in Ca + Sr and the peaks at 471.5 nm due to LICET in Ca Sr system.