Mermaid Saga by Rumiko Takahashi (Volumes 1-3)

"According to an ancient Japanese legend, mermaid flesh may grant immortality if eaten. However, there is a much greater chance that consumption will lead to death or transformation into a damned creature known as a Lost Soul (Deformed Ones in the English dub). Mermaid Saga tells the tale of Yuta, an immortal young man who has been alive for five hundred years after eating mermaid flesh. However, over the years he is grown tired of his immortality and throughout the series, he wanders across Japan searching for a mermaid who may be able to turn him back into a normal human being. He encounters Mana, a young woman who is about to be sacrificed. She has been forced to eat mermaid flesh so that after she is killed, her flesh can be used to rejuvenate a village of ageing immortal women. Yuta rescues her and they travel on together while Yuta pursues his quest to become human again."
- Wikipedia