The invention relates to a process and complete-set apparatus for treatment of tail gases generated during steam blowing. The apparatus comprises a condensation heat exchanger, a three-phase separator, a mixing tank, a vacuum pump, a compression and condensation unit, a gas-liquid separator, membrane assembly, a heat exchanger and a low-temperature catalytic oxidation reactor. The tail gases generated during steam blowing are firstly cooled in the condensation heat exchanger, then the cooled tail gases enter the three-phase separator, and primary separation is performed in the three-phase separator to obtain dirt oil, waste water and waste gases, the separated dirt oil is stored in an oil storage tank, the separated waste water is treated in a sewage pipe network, and the separated waste gases are recycled and treated in a process device integrating a compression and condensation process, a membrane separation process and a low-temperature catalytic oxidation process. According to the invention, when the apparatus is used, higher-value organic materials in the tail gases can be recycled, and the emission indexes of the tail gases can be satisfied, and meanwhile, no electric heating systems are used, so that the explosion-proof grade of the apparatus is improved, and skid-mounted mobile design is adopted, so that requirements of starting the apparatus near petrochemical enterprise equipment can be satisfied, and on-site processing of the tail gases is realized.