Tomoki Sakurai has spent his whole life waking up in tears from the same recurring dream: a mysterious angel he has never met vanishes into the sky, saying, "The sky has captured me." Then, one day, the dream changes—the angel descends from above, desperately pleading for his help.
When Tomoki nods off in class, his childhood friend Sohara Mitsuki shakes him awake and notices his teary eyes. Worried, she insists he talk to Eishirou Sugata, their eccentric upperclassman who is obsessed with "The New Continent"—a bizarre flying phenomenon that no one can explain. As the anomaly is due to pass over their town, Sugata proposes the three meet at midnight to investigate Tomoki's dream and gather data on The New Continent. Only Tomoki shows up, and as he is about to leave, an angeloid falls from the sky, binds herself to him, and declares him her master.
Soon after, Sohara forces Tomoki to join the New Continent Discovery Club, which has Sugata as its sole member. Together, the trio works to unravel the secrets of The New Continent, the angeloids, and the girl from his dreams—but what they uncover may be far more sinister than anyone anticipated.