For as long as he can remember, Tomoki Sakurai has woken up crying to the same dream: an angel he has never met disappearing into the skies, saying, "The sky has captured me." But one day, the dream is different. Now, the angel descends from the skies, desperately asking Tomoki for his help.

After falling asleep in class, his childhood friend Sohara Mitsuki, wakes him up and notices the tears in his eyes. Worried, she has him consult Eishirou Sugata, their eccentric upperclassman who is obsessed with "The New Continent"—a flying anomaly whose existence no-one can explain. With the anomaly set to pass over their town, Sugata decides the trio should meet up at midnight in a bid to solve Tomoki's dream as well as gather more information on The New Continent. Being the only one who showed up, Tomoki is about to leave when an angeloid falls from the sky and binds herself to him, declaring him her master.

Shortly after, Sohara forces him to join the New Continent Discovery Club, whose sole member is Sugata. Together, they work to uncover the secrets behind The New Continent, angeloids, and the girl behind his dreams—but what they discover may be much more sinister than what anyone expected...