The invention discloses an air suction warming heat exchanging method and an air suction warming heat exchanging system of a gas turbine compressor, and belongs to the technical field of gas turbines. The warming method comprises heating air suction of the gas turbine compressor by using exhaust gas from the gas turbine as the heat source. The warming system comprises a gas turbine unit, wherein an air inlet is provided with an air intake filter; an air vent or an air vent successive afterheat utilizing system is provided with a heat recovering device; a heating device is arranged at the air intake filter; and the heat recovering device and the heating device are combined to form a heat exchanging network. According to the air suction warming heat exchanging method and the air suction warming heat exchanging system of the gas turbine compressor, the exhaust fuel gas from the air vent of the gas turbine is used as the heat source to warm the inlet air from the compressor. The air suction warming method and the air suction warming system improve the air intake temperature of the compressor, achieve the purpose of preventing freezing of a filter element of the air intake filter or freezing of an inlet blade of the compressor, improve the economical efficiency of the warming process, and avoid unfavorable influence on the working condition of the gas turbine by the heat recover of the gas turbine body.