A low temperature structure analysis for the alpha'-(BEDT-TTF)(2)IBr2 compound has been carried out. The temperatures studied include the regions where anomalous behavior of the conductivity and the susceptibility exist. It has been found that particular terminal ethylene groups of the BEDT-TTF molecules in the unit cell show anomalous temperature-dependent behavior. An anomalous behavior of the unit-cell parameter gamma has been also observed. These are considered to be related with the anomaly of the conductivity around 200 K. No remarkable change in unit-cell parameters has been observed corresponding to the change of the susceptibility around 60 K. It is possible to calculate overlap integrals between the BEDT-TTF molecules by using low-temperature crystal data. They show characteristic changes among three temperatures 300, 120, and 20 K.