Thousands of years ago, an alien spaceship visited the Earth and became a god to the Aztecs. The aliens fathered the Pumaman, a man-god with supernatural powers who would guard the people of Earth and transmit his powers to his descendants. The original Pumaman was entrusted a gold mask with the ability to control people's minds. In the present day, in London, archaeologist Jane Dobson (Sydne Rome) has found the mask and deciphered its instructions: when aimed at someone, it can be used to control their mind, and the control becomes tighter if a replica of the person's head is wired into it. Her employer, the villainous Dr. Kobras (Donald Pleasence), plans to use it to control the minds of world leaders. He begins with Jane, who is the Dutch ambassador's daughter. Kobras somehow learns the Pumaman will be after the mask, and is an American orphan living in London. Reasoning that the Pumaman can survive great falls, like a cat, he orders his henchmen to throw people matching that description from tall places and see if they survive.