The invention provides a normal putting-into-operation device for realizing denitration at a starting stage by heating fed water and a fume in a close-furnace grading manner. The normal putting-into-operation device for realizing the denitration at the starting stage by heating the fed water and the fume in the close-furnace grading manner comprises a preheating system, a first boiler, a second boiler and a denitration system, wherein a hot secondary air outlet pipeline of the first boiler and a fume outlet pipeline of the second boiler are connected in parallel, and then are connected into the denitration system; the preheating system comprises a steam turbine, a heat exchanger, and a deaerator, a coal economizer and a furnace bottom water-cooled wall lower communicating box, which are communicated in sequence to form a ring; the steam turbine is connected with a high-parameter gas pumping pipeline and a low-parameter gas pumping pipeline respectively; the other end of the high-parameter gas pumping pipeline is connected with the heat exchanger; the other end of the low-parameter gas pumping pipeline is connected with the deaerator; the heat exchanger is arranged in the hot secondary air outlet pipeline of the first boiler; and the coal economizer is arranged in the fume outlet pipeline of the second boiler. By using the device, the temperature of the fume at an inlet of the denitration system can be enabled to reach a lowest putting-into-operation temperature value or above before fuels are put into operation in the boilers; and the normal putting into operation of the denitration system at the starting stage is realized.