Thermal instability in a horizontal layer of nanofluid saturated by anisotropic porous medium is investigated for realistic boundary conditions. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries. The modified Darcy equation that includes the time derivative termused tomodel themomentumequation.Alinear stability analysis based upon normal mode technique is used to study the onset of instabilities of nanofluid saturated by anisotropic porous medium. Rayliegh number on the onset of stationary convection has been derived using Galerkin method and graphs have been plotted for case of stationary convection to study the effects of the thermal anisotropy parameter, mechanical anisotropy parameter, Lewis number,modified diffusivity ratio,porosity and nanoparticles Rayleigh number on stationary convection. Oscillatory convection has been ruled under certain condtion.