A theoretical analysis of buoyancy-driven instability under transient basic fields is conducted in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy's law is used to explain characteristics of fluid motion and the anisotropy of permeability is considered. Under the Boussinesq approximation and the principle of exchange of stabilities, the stability equations are derived by using the linear stability theory and the energy method. The linear stability equations are analyzed numerically by using the frozen-time model and the linear amplification theory and the global stability limits are obtained numerically from the energy method. For the various anisotropic ratios, the critical times are predicted as a function of the Darcy-Rayleigh number and the critical Darcy-Rayleigh number is also obtained. The present predictions are compared each another and with existing theoretical ones.