If the situation of quantum gravity nowadays is nearly the same as that of quantum mechanics in its early time of Bohr and Sommerfeld, then a first-step study of the quantum gravity under Sommerfelds quantum condition of action might be helpful. We present the spectra of quantum Schwarzschild black hole in non-relativistic quantum mechanics. It is found that the quantum of area is 8π/3 l2p the quantum of entropy is 2π/3kB and the Hawking evaporation will cease when the black hole reaches the ground state m = 1/2√3mp.