The invention discloses a convex die mounting structure of a cold stamping die. The convex die mounting structure comprises a die body, wherein a fixing groove is formed in the die body; a convex die is movably arranged in the fixing groove; first channels are formed in the two sides of the fixing groove separately in a symmetric manner; each of the first channels adopts an inverted L-shaped structure; the first channels are formed in the die body; a support pillar is movably arranged in each of the first channels; the support pillars extend into the fixing groove; an extrusion plate is connected to one end of each of the support pillars; the extrusion plates are arranged in the fixing groove; the convex die is movably arranged between the extrusion plates; a connecting piece is arranged at the top end of each of the support pillars; each of the connecting pieces is movably arranged in the corresponding first channel; the connecting pieces extend out of the die body; a reset spring is arranged on one side of each of the connecting pieces. According to the convex die mounting structure of the cold stamping die, the structure is simple, the convex die can be quickly dismantled and replaced, the working efficiency is improved, and the using requirements of people are met.