Gradient distribution of refractive index appears commonly in gas of non-uniform temperature/pressure and water of non-uniform salinity. Efficient and accurate solution of radiative transfer in graded index media is essential for related applications. Finite element method (FEM) is a very effective tool to solve various problems governed with partial differential equations. However, FEM may suffer stability problem for solving radiative transfer in semitransparent media due to the convection-dominated property of the transfer equation. The existence of two angular derivative terms complicates the solution of radiative transfer in graded index media as compared to uniform index media. In this paper, a new stabilized FEM is proposed to solve radiative transfer in multi-dimensional graded index media, based on the second-order form transformation approach. Using the approach, a second order diffusion term is naturally introduced in the transfer equation, which ensures numerical stability, and avoids the false smearing effects as compared to the common schemes based on artificial diffusion. The performance of the presented FEM is verified with one- and two-dimensional test cases. It is demonstrated that the new FEM owns good numerical stability and accuracy, and could potentially be an effective tool to solve radiative transfer in graded index media.