The enzymatic straw material pulping process includes three stages of mechanical pre-treatment, enzyme treatment and chemical pulping or chemical-mechanical pulping. After being pretreated mechanically in a pulp grinder, the straw material is treated with hemicellulase liquid or mixed enzyme liquid comprising hemicellulase and lignin peroxidase at pH 3.5-6.5 and 40-60 deg.c for 1-10 hr. In chemical pulping, the material is presoaked with waste pulp-making liquor before extruding out wastes liquor and digested; and in chemical-mechanical pulping, the material is first treated with EDTA, NaOH and H2O2 at 40-80 deg.c for 30-120 min and then ground to form the pulp. The present invention is used in papermaking enterprises with straw as material and has the advantages of low pollution load, high, paper pulp quality, easy-to-process waste liquor, etc.