A method of manufacturing a continuous curvature convex roll for a continuous casting bloom, wherein: an outer profile curve of a working part of a roll body of the continuous curvature convex roll body is composed of a first straight line section, a first transition curve section, an intermediate straight line section, a second transition curve section, and a second straight line section; wherein the first transition curve and the second transition curve are mirror symmetrical; wherein the first transition curve section, the first straight line section, and the intermediate straight line section have first-order derivative continuity, second-order derivative continuity, and curvature continuity, forming a first transition curve having a continuous curvature; the second transition curve section, the intermediate straight line section and the second straight line section have first-order derivative continuity, second-order derivative continuity, and curvature continuity, forming a second transition curve having a continuous curvature; and when manufacturing and processing the convex roll, a blank is first cast according to shape and size requirements of the convex roll, and then the working part of the roll body is formed by subjecting the blank to rotational processing along a central axis of the convex roll according to a shape of the outer profile curve to form the continuous curvature convex roll; alternatively, for an existing flat roll, a protuberance is first formed on the flat roll at a position corresponding to the working part of the roll body by resurfacing welding, and then the working part of the roll body is formed by subjecting the protuberance to rotational processing along a central axis of the convex roll according to a shape of the outer profile curve to form the continuous curvature convex roll. an outer profile curve of a working part of a roll body of the continuous curvature convex roll body is composed of a first straight line section, a first transition curve section, an intermediate straight line section, a second transition curve section, and a second straight line section; wherein the first transition curve and the second transition curve are mirror symmetrical; wherein the first transition curve section, the first straight line section, and the intermediate straight line section have first-order derivative continuity, second-order derivative continuity, and curvature continuity, forming a first transition curve having a continuous curvature; the second transition curve section, the intermediate straight line section and the second straight line section have first-order derivative continuity, second-order derivative continuity, and curvature continuity, forming a second transition curve having a continuous curvature; and when manufacturing and processing the convex roll, a blank is first cast according to shape and size requirements of the convex roll, and then the working part of the roll body is formed by subjecting the blank to rotational processing along a central axis of the convex roll according to a shape of the outer profile curve to form the continuous curvature convex roll; alternatively, for an existing flat roll, a protuberance is first formed on the flat roll at a position corresponding to the working part of the roll body by resurfacing welding, and then the working part of the roll body is formed by subjecting the protuberance to rotational processing along a central axis of the convex roll according to a shape of the outer profile curve to form the continuous curvature convex roll.