We discuss the possibility of the non-perturbatively renormalizable quantum gravity which is called asymptotically safe gravity. The functional renormalization group method is used to analyze the system. I first review the basic ideas of the asymptotically safe gravity and the functional renormalization group. After that, we consider the asymptotic safety scenarios of the scalar-gravity system and the Higgs-Yukawa one coupled to quantum gravity. It is shown that the fermionic fluctuation makes the scalar mass and non-minimal coupling irrelevant. With this in mind, we discuss the hierarchy problem and the possibility of large non-minimal coupling.