The present method of constructing block pavement, which solves conventional problems, is applicable not only to landscape pavement of a sidewalk or an open space, but also to an ordinary roadway having heavy traffic of large vehicles, and makes available block pavement provided with a beautiful appearance and an excellent durability. This method involves the steps of providing a tack coat layer by spraying an asphalt emulsion on a base of a road or the like; then placing an aggregate on the upper surface thereof to form an aggregate layer; arranging a plurality of paving blocks on the upper surface thereof while keeping the upper surfaces of the blocks in flush; then pouring uniformly a cement asphalt mortar from joint spaces formed between the paving blocks to fill the void of the aggregate layer to form a buffer support layer; and filling also the joint spaces uniformly with the cement asphalt mortar or a pouring joint filler material other than the cement asphalt mortar, thereby securing the paving blocks integrally on the base.