Disclosed is a method for constructing an expansion joint of a bridge or a underground road way structure having a concrete structure and a road pavement layer formed on the concrete structure including: a block forming step of forming an expansion joint opening with a predetermined width in the concrete structure and forming a block on the road pavement layer in such a way that the block is located corresponding to the expansion joint opening and is wider than the expansion joint opening; a first elastic material inserting step of inserting an elastic material into the expansion joint opening; a first sealant coating step of coating primer on all exposed surfaces of the block, and coating asphalt-based sealant with high adhesive properties and weather resistance on the primer, and filling an area from the expansion joint opening to a place above the elastic material with sealant; a support plate mounting step of putting a support plate on the sealant to cover the expansion joint opening; a second sealant coating step of coating asphalt-based sealant with high adhesive properties and weather resistance not to expose the support plate to the outside; a mixture layer forming step of filling the block with mixture in which the asphalt-based sealant with high adhesive properties and weather resistance and dried aggregate are mixed; a third sealant coating step of coating asphalt-based sealant with high adhesive properties and weather resistance on the mixture layer; a hole forming step of forming a hole which is located to be spaced apart from the block; a second elastic material inserting step of inserting an elastic material into the hole; and a sealant injection step of injecting asphalt-based sealant with high adhesive properties and weather resistance into the hole. [Reference numerals] (AA,GG) Expandable and contractable joint material; (BB,HH) Asphalt pavement layer; (CC) Deck coating agent; (DD) Underground concrete structure; (EE) Expansion joint; (FF) Longitudinal section view of an underground road way; (II) Waterproof material and primer; (JJ) Concrete floor plate; (KK) Mounting of the joint; (LL) Longitudinal section view of a bridge