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