The electron paramagnetic resonance of the Cr3+ ion in an alexandrite single crystal was explored. The angular dependence of the resonance fields observed using an X-band spectrometer in the crystallographic planes were analyzed using the monoclinic spin Hamiltonian. The spectroscopic splitting tensors g(i) and the 2nd order zero field splitting parameters vertical bar D vertical bar and vertical bar E vertical bar for the Cr3+ center at Al3+ site with mirror symmetry (C-s) in an alexandrite crystal were calculated using the crystal field theory for C-s symmetry. Then, the theoretical values were compared with the experimental values. The calculated spin Hamiltonian parameters explain nicely the experimental parameters for the Cr3+ center with mirror symmetry.