Taiyou no Uta
A Song to the Sun

Drama Wiki said:
While working at a seaside inn with his high school buddies, Kouji Fujishiro (Yamada Takayuki) meets Kaoru Amane (Sawajiri Erika), a street musician. Kaoru is suffering from an incurable disease called XP (xeroderma pigmentosum), and can?t be exposed to the sun. Under the sun, the two would never have met. Still, destiny brings the two together. Since the day he suddenly lost his job, Kouji has lost sight of his dreams. But when he meets Kaoru, who is making positive efforts to become a singer, Kouji regains his long-forgotten passion for music.
Has 10 episodes.

It's the type of Romance/Drama that has both Lightheartedness and strong emotional impact. The theme alone shows how romantic it is: About a girl that sings under the moonlight.

Later on in the show, Kaoru, Kouji and his friends, forms a band known as Moon child.

http://wiki.d-addicts.com/Taiyou_no_Uta