The invention discloses hot-distribution rubber bituminous pavement and a construction method thereof. The construction method comprises the following steps: 1, cleaning a lower bearing layer; 2, preparing rubber asphalt; 3, distributing the rubber asphalt, namely, uniformly distributing a rubber asphalt layer on the lower bearing layer, wherein the distribution amount of the rubber asphalt is 2.2 to 2.6 kg/m<2>, and the distribution temperature is 180 to 190 DEG C; 4, distributing broken stone with an amount which is 60 to 70 percent based on the distribution area of the rubber asphalt, wherein the distribution temperature of the broken stone is not lower than 80 DEG C; and 5, rolling and forming, namely, rolling and forming a rubber asphalt waterproof adhesive layer by a rubber-tire pavement roller following a broken stone distribution vehicle, wherein the rubber-wire pavement roller rolls the pavement once to twice back and forth. The construction method of the invention can enhance the inter-layer adhesive performance, prevent water penetration, effectively absorb and eliminate inter-layer stress and reduce reflection cracks caused by the conventional bituminous pavement, and can be applied to the projects of building and rebuilding bituminous pavement, pavement of bituminous concrete bridge floor, bituminous overlaying of cement concrete pavement and the like.