This study presents the reflection and transmission characteristics of Laguerre Gaussian beam (LGB) from the periodic layered film with topological insulator (TI) based on angular spectrum expansion and 4×4 matrix transfer theory. For the incidence of linearly polarized LGB on the periodic layered film, the intensity distributions of the reflected and transmitted fields are evaluated and discussed. It is shown that the intensity distributions are greatly influenced by the topological magneto-electric polarizability (TMEP) of TI and the periods of the TI periodic layered film. This investigation provides a new method to manipulate the light field of vortex beams by changing the TMEP value or the periods of TI films. The methods presented herein can be extended to different TI-layers and provide reference for the research on photonic band structures and band gaps in TI photonic crystals in further research.