The invention relates to a mass and heat transfer device combining an absorbing tower and a heat exchanger and an operating method of the mass and heat transfer device, and belongs to the field of gas discharging technologies for chemical engineering, petrochemical engineering, environmental protection, medicine and the like. An upper shell cover is disposed on the top end of pipe bundle. The right side of the top end of the upper end shell cover is provided with a gas outlet. The top end of the upper end shell cover is provided with an absorbent inlet tube. A side of the upper end of the pipe bundle is provided with a cooling water inlet. A side of the lower end of the pipe bundle is provided with a cooling water outlet, and the other side of the lower end of the pipe bundle is provided with a water outlet. The bottom of the pipe bundle (7) is provided with a lower shell cover. A side of the lower shell cover is provided with a gas inlet. The lower end of the lower shell cover is provided with a liquid outlet. Five baffle plates with one-fourth gaps, and two pipe plates are disposed between an upper sieve plate and a lower sieve plate. A plurality of heat exchanging pipes, arranged in regular triangles, are disposed between the two pipe plates. The heat exchanging pipes are filled with packing having the diameter of 1.5mm-2.0mm.