According to the beam transmission theory in uniaxial crystal, the analytical expression of Airy-Hermite-Gaussian beam (AiHGB) with a cross phase propagating in uniaxial crystal is obtained. The numerical simulation results show that AiHGB with initial cross phase is still linearly polarized, but not necessarily transmission invariant. Specifically, depending on the cross phase coefficient, beam parameters, and crystal material parameters, the initial cross phase will cause AiHGB spot to rotate continuously, and the total rotation angle is 90° in the whole transmission process from near field to far field. When the cross phase coefficient is large enough, the AiHGB spot only rotates; When the cross phase coefficient is appropriate small, the AiHGB spot not only rotates in orientation, but also changes in spot shape.These results show that by properly selecting the crystal material (i.e. refractive index) and the coefficient of additional cross phase factor, the orientation and structure of beam pattern shape can be accurately adjusted, and the refractive index of crystal material can be determined or the coefficient of cross phase factor can be measured.