Devils' Line 

Tsukasa, a college student, is rescued from an attack by a devil, one of many vampires that can blend in among the human population. Anzai, her savior, is a half-devil who exploits his supernatural gifts as a member of a shadowy police task force that specializes in devil-related crime in Tokyo. As Anzai continues to keep guard over Tsukasa, the two quickly forge a tentative bond—one that Anzai fears will test his iron-clad rule of never drinking human blood... (Source: Kodansha USA) Note: Includes 11 extra chapters.