The photo-ionization cross sections of the 11S and 21S states of He were evaluated in the energy regions 0.20-2.40 Ry and 3.15-3.30 Ry. The 56-term 1S bound-state wave functions obtained by Pekeris were used for the initial states. An expansion into a complete discrete basis set (a modification of the close-coupling method used in electron-atom scattering) was carried out for the 1P final-state continuum wave functions. Particular attention was given to the processes where the ejected photoelectron leaves the He+ ion in an n=2 excited state. The results obtained from the length and velocity expressions for the photo-ionization cross sections show an agreement to within 1% in the lower-energy region. Good accuracy is achieved for the negative-power moments of the oscillator-strength distributions.