In this paper the characteristics of dispersion relation and nature of magneto hydrodynamic anisotropic instabilities are investigated in collisionless, homogeneous, and magnetized plasma. The basic equations are derived and linearized for small perturbation under the assumption that the plasma is drifting for MHD by using the moments of the Boltzmann -Vlasov transport equations. After that the dispersion relation is derived and parallel and perpendicular wave modes are discussed. From the investigation of energy principle due to drift, different nature of MHD anisotropic instability criteria are discussed. Comprehensive analytical and numerical studies of the dispersion relation have been made to understand the modes of propagation of the waves in drifting and non-drifting plasma. Finally the instability criteria of nature of MHD anisotropic instabilities are derived and discussed.

Keywords: MHD (Magneto hydrodynamic), CGL (Chew, Goldberger and Low), Plasmas, Waves, instabilities