NO, it is not finished.
The anime finished before the manga:
Anime finished: June 18, 2010
Manga finished: February 03, 2011
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B-gata H-kei follows Yamada, a high school girl with a secret and unusual goal: to experience sex with one hundred different men.
However, her friend points out a major problem: Yamada is a virgin, and incredibly awkward around men. Her insecurity about her own body contributes to this awkwardness.
To overcome this, she decides her first experience must be with another virgin. She then sets her sights on the shy and kindhearted Takashi Kosuda as her ideal first target.
The anime revolves around Yamada's attempts to seduce Kosuda, facing rivals for his affections and her own growing feelings along the way. As she tries to achieve her goal, she begins to genuinely enjoy spending time with him.