Under the condition of turbulent freezing, the theory model of inversing the vertical distribution of transverse wind speed is proposed by using space-time cross correlation function of two position detection jitter signals. Two parameters of this model are turbulence profile and derivation of cross correlation function at the delay time of zero. Supposing that transverse wind speed is accord with Gauss model, numerical simulation is carried out with genetic algorithm. Through the inversion calculation of two typical turbulence models, it’s found that the inversion wind profiles are coincide with the theoretical wind profiles, and the relative error is not more than 3.3% and 1.6%, respectively. The characteristic height of the turbulent profile is changed and inversion calculation is carried out. Results show that when there is a large error in the turbulence intensity, the model can still be applied to inverse vertical distribution of transverse wind speed in the lower layer.