The invention discloses a working method of an external heating surface cooler drying device. The liquid oil, water and solid particles in raw material gas are removed by means of a pre-filter and a precision filter, the raw material gas then enters an absorption tower A in a full flow through a valve, and the raw material gas becomes dry gas since the moisture in the raw material gas is absorbedby an adsorbent and is then discharged through a post-filter; in an absorption process of the absorption tower A, pressure relief, heating, blow-cooling, replacement and pressure equalization are carried out in an absorption tower B, and the working states of a drying tank A and a drying tank B are then switched; the drying tank B performs absorption work, and the drying tank A performs regeneration work. After the working method of the external heating surface cooler drying device is adopted, remarkable energy saving and consumption reducing effects can be achieved, the energy needed by the regeneration of the adsorbent is greatly reduced, the dew point of the finished product gas is enabled not to drift, and the cost is greatly lowered.