On the basis of dynamic quantization method we build in this paper a new mathematically correct quantization scheme of gravity. In the frame of this scheme we develop a canonical formalism in tetrad-connection variables in 4-D theory of pure gravity. In this formalism the regularized quantized fields corresponding to the classical tetrad and connection fields are constructed. It is shown, that the regularized fields satisfy to general covariant equations of motion, which have the classical form. In order to solve these equations the iterative procedure is offered.