PROBLEM TO BE SOLVED: To provide a building support structure with which reinforcement of the foundation of a building can be appropriately performed, a construction method of the same, and a pile cover used in the building support structure and the construction method.SOLUTION: A construction method of a building support structure 10 forms a pile foundation 12 by driving support piles 11 into a plurality of positions of the ground, forms a leveling concrete layer 15 on the pile foundation 12, performs marking on an upper surface 15M of the leveling concrete layer 15, and forms a foundation 40 of the building on the leveling concrete layer 15. Specifically, the construction method attaches a centering bolt 23 which vertically moves on the central axis 11J of the support pile 11 to the upper part of each support pile 11 before forming the leveling concrete layer 15, adjusts the upper ends of the plurality of centering bolts 23 to the same height position, and makes the upper surface 15M of the concrete match w
