The vortex beam has special dynamics and quantum properties, so it has great research value in the field of communication and medicine. These properties are closely related to its unique phase structure. With the deepening of research, the propagation characteristics of vortex beams in the medium have also received extensive attention. This paper mainly studies the phase characteristics of vortex beams in layered media. Taking the linearly polarized vector Laguerre-Gaussian beam as an example, according to the method of transmission matrix, wave decomposition and Lorentz transformation, we analyze its phase change in free space, single-layer medium, high-speed moving medium and multi-layer medium. It is found that the phase rotation direction of the reflected vortex beam and the transmitted vortex beam is related to the wave vector, and the phase structure will change with the change of the incident angle.