In order to solve the problem that the traditional stress cone adopts the straight cone curve, which is easy to cause the uneven distribution of the electric field inside the cable intermediate joint, a quadratic cone curve stress cone was designed by using the number-shape combination method. Firstly, the 35 kV cable intermediate joint model was established. Secondly, the electric field distribution characteristics of the stress cone with the straight cone curve and the quadratic cone curve were compared and analyzed. Finally, the key structural parameters such as the winding insulation thickness, cone length, stress cone thickness and cone head curvature radius of the quadratic cone curve stress cone were designed. The results show that compared with the straight cone curve stress cone, the maximum electric field strength inside the joint of the quadratic cone curve stress cone can be reduced by 47.43% at most. When the stress cone winding insulation thickness, cone length, cone curvature radius and stress cone thickness are 10.94 mm, 50.48 mm, 2.3 mm and 3.3 mm, respectively, the maximum electric field strength inside the joint can be reduced to 3.32 kV/mm, and the maximum electric field strength of the cone surface can be reduced to 1.67 kV/mm. The parametric design of the quadratic cone curve stress cone can more effectively uniform the internal electric field of the joint, reduce the possibility of partial discharge, and improve the operation reliability of the joint. It has reference value for the optimal design of the cable intermediate joint stress cone.