Topological insulator Bi2Te3 crystals were grown and their thermal expansion was studied with X-ray diffraction at various temperatures. It was shown that the linear thermal expansion coefficients, || and , which reflect, respectively, the thermal expansion within and out-off a-a plane of the Bi2Te3 crystal, exhibit quite different temperature dependent features. The obeys the Debye law in a relatively wide temperature range, while || deviates qualitatively from the Debye law at 100 K. Possible mechanisms behind the observed phenomena were explained using the crystal structure and the bonding features between the atoms in Bi2Te3 crystal.