The Jahn-Teller effect is a geometrical distortion which lowers the system symmetry and lifts orbital degeneracy in molecules and solids. It affects a wide range of properties, including magnetic and band structures. In this work we propose a family of Cr-containing intrinsic magnetic topological insulator materials which are subjected to a pseudoJahn-Teller effect.CrBi2Se4, CrBi2Te2Se2, and CrBi2Te4. Using first-principles calculations we study their properties and investigate the impact of Jahn-Teller distortions on the electronic and magnetic properties. We show that these distortions can significantly affect magnetic anisotropy energy and band structure. Without the distortions accounted for, all three of the compounds exhibit a semimetallic band structure. The distortions open a band gap, which in the cases of CrBi2Te2Se2 and CrBi2Te4 is inverted. We also investigate the CrBi2Te2Se2 and CrBi2Te4 surface band structure and demonstrate that the surface states have a topological origin.