The instability induced by external gravitational forces in an infinite, stratified, anisotropic plasma with a magnetic field has been studied using the Chew, Goldberger, and Low approximation. A plasma whose equilibrium properties vary with height in a horizontal variable magnetic field and a vertical gravitational field is considered. Three stability criteria are derived from the energy principle, two of which lead to the ``firehose'' and ``mirror'' instabilities found in a uniform anisotropic plasma while the third criterion is for the convective instability arising from gravity. In contrast to the isotropic case, it is found that the convective criterion depends explicitly upon the magnetic field. An increase of the magnetic field by a constant quantity shows that the plasma is more stable. The growth rates of the unstable displacements in the least stable regions are calculated using a normal mode analysis.