Grandidierite, a rare mineral with ideal chemical formula (Mg, Fe)AI3SiBO9 was discovered in 1987 in Jixi County, Heilongjiang Province. X-ray diffraction analysis and transmission electron microscopic study (TEM)of the mierostructure of grandidierite show that this mineral belongs to orthorhombic system with the unit cell parameters a=10.318(2)A, b=10.981(1A), c=5.753(1)A and the space group Pbnm. Microstructural analysis of the complex (high-order) twins is very complicated, Formerly, much study was devoted to simple high-order twins existent in metal materials and minerals, with less attention paid to the study of the complex (high-order) twins in the low symmetrical minerals. When studying the microstucture of grandidierite by means of TEM in our laboratory, we discovered for the first time complex (high-order) twins in the mineral and obtained the selected area electron diffraction (SAED) and the electron micrograph of the high-order twin. The SAED and the bright field image of TEM have been used jointly to determine the complex (high-order) twins in grandidierite, i.e., (202) growth twin, (280) (202) sec3ndary order twin, (041)(280)(202) third order twin, and (443) fourth order twin. The structural relationship between the complex (high-order) twins in the mineral has been illustrated, and the analytical method for the microstruetures of the minerals with low symmetry and complex (high-order) twins has been summarized. Experimental results show that there are splits of electron diffraction spots in four directions, i.e., along [202], [280]T, [041](TF), [443], suggesting that there are plane defects on the crystallographic planes (202), (280)T, (041)(TF), (443) in the mineral. The discovery and study of the microstruetural characteristics of the low symmetrical and complex (high-order) twins in borate mineral have furnished new data to modern mineralogy.