Abstract: In this paper, the hyperspherical coordinates are used to describe the Schrodinger equation of He and H^-.The equation of motion of two-electron atom in 3-Dspace is transformed into that of one-electron atom in 6-Dspace, subjected to generalized Coulombic potential.The cigenfunctions of the generalized angular momentum operator are used as a basis set for the hyperspherical wavefunc-tion, with which a coupled differential equation of hyperradial wave-function is obtained, By describing the hyperradial wave-function with generalized Laguerre polynomials, a secular equation is gotten for the non-orthogonal basis set of hyperradial wavefunction by means of linear variational method.The calculated ground state energies of He and H^- agree well with precise values.

Key words: Hyperspherical coordinates, Linear variation, Non-orthogonal basis set