Urushiba Rinka, a fairly normal high school girl, leads a rather penniless life together with her father, her only family. This forces Rinka to work as a waitress after high school to raise money for them to secure rent and food.
One day, she notices a flying penguin, Peggy, and follows it to the Tokyo Skytree, where swarms of glowing fish just swim through thin air. Azuma Kyoutarou, a boy from her school, also happens to be there, confirming that all this is not a hallucination. Contact with one of these fishes causes Rinka to pass out. Surprisingly, when she wakes up again, she has developed the power to move through inanimate objects such as the floor of her apartment. And she is not the only one to gain such extraordinary powers: Kyoutarou can teleport, and her father has developed very strong magnetic powers.
A series of unexplained art robberies puts Rinka and Kyoutarou on that case, using their ESP powers to take on individuals, who have decided to use their powers for evil. This is how they encounter Kuroi Kobushi, the so-called Black Fist, a thief out to make a name for herself using invisibility. However, there is an organization with far grander and more sinister plans employing strong ESP fighters to secure their version of a new world order.