  Recently proposed quantization in field theory based on an analogue of
Hamiltonian formulation which treats space and time on equal footing (the
so-called De Donder-Weyl theory) is applied to General Relativity in metric
variables. We formulate a covariant analogue of the Schroedinger equation for
the wave function of space-time and metric variables and a supplementary
``bootstrap condition'' which enables us to incorporate classical metric
geometry as an approximate notion - a result of quantum averaging - in the
self-consistent with the underlying quantum dynamics way. In this sense an
independence of an arbitrarily chosen metric background is ensured.
