The 4T2,4T1, and 2E levels of Cr3+ ion on the mirror-site in an alexandrite crystal are in relation to the laser operation of that material. The 4T2 (or 4T1) level splits into three sublevels. In order to determine the energy levele diagram of Cr3+ ions in chrysoberyl, the splitting of the 4T2 and 4T1 are calculated. We have discussed the anisotropic transition intensities of corresponding absorption bands and have found a method to fit the spectra. Furthermore, the values of the parameters K1 and K2 that represent the magnitude of the splitting are obtained, and the crystal field energy level diagram of BeAl2O4:Cr3+(II), labelled by the irreducal representations of point group C3, is given.