Gal Samurai 

The manga's star is Ran Kirishima. She's a junior in the Maizono High School, and a "gal"—a fashionable girl who hangs out in Tokyo's Shibuya district. Ran is originally from Tokyo but when her parents experienced marital trouble, they left Ran in the care of her grandparents in the country side. It was there that her grandfather, a martial arts master, began training her as a martial artist.