The present process is directed to the efficient recovery of helium gas from gas streams which contain about 25 percent by volume or more helium. The process comprises two stages of pressure swing adsorption, each stage being comprised of a plurality of interconnected adsorbent beds. In the first stage of pressure swing adsorption which is comprised of about five phases, the helium content of the gas stream is increased to 95 percent by volume or more. A secondary product gas stream from the first stage of pressure swing adsorption is fed to the second stage of pressure swing adsorption. The second stage of pressure swing adsorption increases the helium content of this primarily non-helium product gas to more than about 50 percent by volume. This gas now with a helium content of more than about 50 percent by volume is fed along with the gas stream as the input gas to the first stage of pressure swing adsorption.