Makai Toshi Shinjuku
English name: Demon City Shinjuku
Genres: Adventure, Horror, Romance, Supernatural
Type: OVA, Episodes: 1
Aired: Oct 25, 1988
Studio: Madhouse
Source: Novel
Rating: R - 17+ (violence & profanity)
Synopsis:
Kyoya's father was a great warrior, killed at the hands of the diabolical psychic, Rebi Ra, who has now opened a portal to hell in the city of Shinjuku. It falls to Kyoya to finish what his father started and battle his way through demons, while protecting a young woman from harm. The only problem is that he's not exactly your classic hero type, and his powers are still latent. 

(Source: ANN)