A support structure of a coke drum including a cylindrical drum body, an inverted-cone-shaped bottom plate connected to a bottom of the drum body, and a cylindrical skirt supporting the drum body includes an annular joining piece joining the drum body, the bottom plate, and the skirt to one another. The joining piece is a unitary member including an upper body part joined to a lower end of the drum body, a lower inner leg part joined to an upper end of the bottom plate, and a lower outer leg part joined to an upper end of the skirt.