Scintillation is an important problem for laser beams in free space optical (FSO) communications. We derived the analytical expressions for the scintillation index of a Gaussian Schell-model beam with cross phase propagation in a turbulent atmosphere. The numerical results show that the quadratic phase can be used to mitigate turbulence-induced scintillation, and the effects of the turbulent strength and beam parameters at the source plane on the scintillation index are analyzed. The variation trend of the experimentally measured scintillation index is consistent with the numerical results. Our results are expected to be useful for FSO communications.