The invention discloses pervious concrete and a construction method thereof. The pervious concrete comprises the following raw materials in percentage by weight: 13.1-15.9% of cement, 12.7-15.6% of river sand, 59.6-66.0% of stones, 3.7-3.9% of water and 4.5-5.0% of admixtures, wherein the admixtures comprise the following raw materials in percentage by weight: 45-50% of ultrafine mineral powder, 15-20% of heavy calcium carbonate, 15-20% of gypsum powder, 3-5% of polypropylene fiber, 5-10% of a polycarboxylate water reducing agent, 4.2-8.4% of adhesive powder and 2-5% of a pigment. The pervious concrete provided by the invention has relatively high water permeability, strength and durability; after the pervious concrete is applied to a practical engineering, the pervious concrete can greatly improve the problem of poor drainage of a hardened road surface, so that the development of the pervious concrete can be promoted.