The invention discloses a catalytic system and a process for the desulfuration of industrial sulfur-bearing waste gas. The catalytic system comprises, by weight percent, 2-50 % of polyhydric alcohol, 1-40 parts of acid catalyst, and the balance of water. The acid catalyst is one or combination of inorganic acid, inorganic acid/slat, and organic carboxylic acid or soluble salt thereof. The process includes: waste gas pretreatment, absorption reaction and sulphur recovery. Low-temperature aqueous phase reaction is applied in the reaction process, and low temperature ensures deep conversion between hydrogen sulfide and sulfur dioxide (total desulfuration rate is increased to 99.95%). The catalytic system is simple to prepare and low in cost.