Based on a manga by Kimura Tahiko serialised in Gangan Wing.

Nagasumi visits his grandmother near the sea during the summer. While visiting, he goes for a swim, and drowns right after entering the water. Fortunately for him he is saved by a young mermaid. Later as he tells the story to his family, a young girl named San appears at his home and begs Nagasumi to marry her.

She's followed by two large thugs and they take both him and his parents to Sans home under the sea. If that wasn't strange enough, it turns out Sans parents are mob bosses. Nagasumi is left with the choice of either death or marrying San. He chooses to marry a mermaid.

This would likely be that, except Sans father and some members of the mob are not exactly thrilled to have Nagasumi courting San and are determined to bring an end to their relationship--or him. And there is also the matter of keeping it a secret that San is a mermaid.