The Goos-Hnchen(GH) lateral displacement and Imbert-Fedorov(IF) transverse displacement of a linear polarized wave at the interface of topological insulator and chiral metamaterial was investigated. Based on the modified energy flux method, the expressions of the spatial shifts were derived, and the relations between the shifts and the incident angle, topological magnetoelectric coupling effect, chiral parameter were also numerically discussed. It is found that, for a linear polarized TE beam, the magnetoelectric couplin effect of the topological insulator or the chirality of the chiral medium has consistent influence on both the two shifts, that is, the topological magnetoelectric coupling can generally suppress both the GH and IF shifts, and the chirality may monotonously enhance or suppress both the two shifts. When gradually enhancing the topological magnetoelectric polarizability, the GH and IF shifts of the linear polarized TM incident wave will be firstly increased, and then it will be suppressed. There exists an extreme displacement. The increase of chiral parameters makes this extreme displacement move towards the smaller value of the magnetoelectric polarizability; Although the influence of chiral parameters on the shifts is generally monotonic, but it is special in certain cases, for example, in case of the GH shift of a right-handed circularly polarized wave, during the period when the topological magnetoelectric coupling increases the shifts, the chirality will also show the enhancement, while in the stage of shift suppression by topological effect, the chirality may suppress the shifts in the meantime. The research on the GH and IF shifts at the interface of topological insulator and chiral metamaterials may develop a new way to control the GH and IF shifts. It also provides an optical method for measuring the topological magnetoelectric coupling and chiral electromagnetic cross-polarization.