Abstract: A highly flexible method for constructing the leading and trailing edges of airfoils plays a significant role in the design and optimization of turbomachinery blade profiles. This paper investigates a multi-degree-of-freedom approach for shaping the leading and trailing edges based on the classical NURBS representation framework, incorporating the geometric characteristics of conic sections and circular arcs. The proposed method enables effective control over the leading and trailing edge profiles by flexibly adjusting the slope, taper, and size of the conic section using only a few parameters, while maintaining the aerodynamic chord length of the blade row and ensuring G¹ continuity at the junctions between the fillet curves and the suction/pressure side curves. Control points and weights are computed based on the specified fillet type and central angle to precisely construct conic sections satisfying convex hull requirements. Furthermore, the fillet parameters are linked to the number of blade sections along the spanwise direction, allowing for dynamic variation of the fillet geometry and enabling efficient parametric modeling of complex 3D blade leading and trailing edges. Numerical simulations demonstrate that, compared with the original airfoil, transonic blades incorporating the proposed edge construction method exhibit significantly improved isentropic compression efficiency and a noticeable weakening of shock waves in the leading-edge region.