More and more multi-component seismic data have been acquired in land and offshore, since multi-wave is beneficial for structural imaging, fluid detection, and reservoir monitoring. Because S-waves are typically influenced by anisotropy in the medium than P-wave, the anisotropy can't be ignored during the converted PS-wave imaging. Gaussian beam migration, as an elegant and efficient depth migration method, has becoming a hot in the study of PS-wave migration, with its accuracy comparable to wave equation migration and flexibility comparable to Kirchhoff migration. In this paper, we introduce an anisotropic Gaussian beam prestack depth migration (GB-PSDM) method for the converted PS-wave, of which the anisotropic media can be a transversely isotropic (TI) media with a symmetry axis vertical or tilted. Based on the anisotropic kinematic and dynamic ray tracing, we present the PS-wave common shot gathers GB-PSDM imaging condition and derive the P-and SV-waves ray tracing in two-dimensional TI media. Tests of numerical models show that the method introduced here is accurate and efficient for the converted PS-wave imaging.