We formulate a model for quantum gravity based on the local-Lorentz symmetry and diffeomorphism. A key idea is the irreversible vierbein postulate that a tree-level action for the model at a certain energy scale does not contain inverse vierbein. Under this postulate, only the spinor becomes a dynamical field and no gravitational background field is not introduced in a tree-level action. In this paper, after explaining the transformation rules of the local-Lorentz and diffeomorphism transformation in detail, a tree-level action is defined. We show that fermionic fluctuations induce a non-vanishing gravitational background field.