The power series method has been adapted to compute the spectrum of the Schrodinger equation for central potential of the form V(r)=d_-2 r^2+d_-1 r+∑_i=0^∞ d_ir^i. The bound-state energies are given as zeros of a calculable function, if the potential is confined in a spherical box. For an unconfined potential the interval bounding the energy eigenvalues can be determined in a similar way with an arbitrarily chosen precision. The very accurate results for various spherically symmetric anharmonic potentials are presented.