So... is Idol Project finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Idol Project follows Mimu, a young girl who dreams of becoming an idol like the beloved President of Earth, Yuri.
She travels to the Starland Festival to audition, but her attempts are constantly thwarted by comedic mishaps.
Along the way, she encounters and befriends the current generation of popular idols who help her out of her predicaments.
Just as Mimu finally gets her chance to shine on stage, she and the other idols are suddenly kidnapped by mysterious aliens.
Mimu must now rise to the occasion and find the strength to save everyone and possibly the world.