  Analytical solutions of the N-dimensional Schr\"odinger equation for the
newly proposed Varshni-Hulth\'en potential are obtained within the framework of
Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the
centrifugal barrier. The numerical energy eigenvalues and the corresponding
normalized eigenfunctions are obtained in terms of Jacobi polynomials. Special
cases of the potential are equally studied and their numerical energy
eigenvalues are in agreement with those obtained previously with other methods.
However, the behavior of the energy for the ground state and several excited
states is illustrated graphically.
