The science fantasy story Tokyo ESP begins with Rinka, an extremely poor high school girl who lives with just her father in modern Tokyo. One day, she is going home from school when she chases a "flying penguin" to the top of New Tokyo Tower—only to have "fish swimming in the air" suddenly appear before her. One of the fish goes through Rinka and gives her extraordinary powers beyond those of normal humans, particularly the ability to slip through solid objects.

Tokyo ESP begins with Rinka Urushiba as a fairly normal high school girl, though she is a bit poor and her only family is her father. This forces her to work as a waitress after high school to raise money for them to secure rent and food. One day, she sees a penguin and some glowing fish swimming through the sky. Rinka might have thought it was a hallucination if there had not been another witness with her, a boy from her school with a strangely scratched-up face. Contact with a fish causes her to pass out, and when she awakens, she has developed the power to move through inanimate objects such as the floor of her apartment. She meets a fellow high school student named Kyotaro Azuma, who has the ability to teleport. The two of them use their ESP powers to take on individuals who have decided to use them for evil. However, there is an organization that plans for a bigger scheme to secure utopia with their ranks consisting of strong ESP fighters and users.