In this paper, using the exponential function transformation, the radial Schrdinger equation with the Hulthén potential is transformed into a hypergeometricdifferential equation under the condition that an effective approximation as 1/r2≈λ2e-λr/(1-e-λr)2 is used for the centrifugal term in the case of any l-states. The exact solution of s-wave scattering state and the approximate analytical solution of non-s-wave scattering states for the Schrdinger equation with the Hulthén potential are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale" and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.