Abstract: The influences of non-homogeneous stratification on energy propagating path of internal gravity waves are discussed by using WKB approximation. The conditions of conservation of generalized energy,action and enstrophy are obtained. A necessary condition for instability of internal gravity wave is derived. The equation governing refraction of wave rays and two kinds of critical layer are also yielded. Finally,the wave rays for different stratifications are calculated by using a Runge-Kutta method.