All-electron full potential calculations based on spin density functional theory were performed to study cubic zincblende (ZB) and hexagonal NiAs structures of bulk CrTe and ZnTe/CrTe(0 0 1), CdTe/CrTe(0 0 1) and CdSe/CrTe(0 0 1) interfaces. The lattice mismatch effect in ZB CrTe and magnetic properties of CrTe in the ideal ZB CrTe structure were investigated. The band alignment properties of the ZnTe/CrTe(0 0 1), CdTe/CrTe(0 0 1) and CdSe/CrTe(0 0 1) interfaces were computed and a rather large minority valence band offset of about 1.09 eV was observed in ZnTe/CrTe(0 0 1) heterojunction. Also in the CdTe/CrTe(0 0 1) and CdSe/CrTe(0 0 1) interfaces, the conduction band minimum of minority spin in CrTe was above the conduction band minimum of CdTe and CdSe and so the majority spin electrons could be directly injected to both semiconductors, indicating the possibility of highly efficient spin injection into the CdSe and CdTe semiconductors.