The story settings takes place on Earth, where alien attacks have turned into everyday sights instead of mere rare phenomenon. All countries around the world have united their efforts to develop effective counter measures against the aliens' attack, but all without success.
In Japan, there is a secret organization called GRA (GRAND REFLECT AMUDO) under Alien Defense Agency direct control. The main purpose of this organization is to find a special counter measure against alien attack, with help from Dr. Sanada Mio.
Dr. Sanada Mio invented a next-generation weapon called "G-on" to repel the aliens' attack. This new secret weapon needs to resonate with the heart of its user (has to be a young girl! You know the Japanese anime/manga common approach for transformation bigrazz), and it will turn into a sword which holds power proportional to the strength of the heart of the girl who uses it. Needless to say, the new weapon and the plan are approved immediately, and a special school is established to recruit and train young girls from across the country.