As high homogeneity in magnetic field is required to increase the resolution of MRI magnets, various shimming methods have been researched. Using one of them, the design of the superconducting active zonal shim coil for MRI magnets is discussed in this paper. The magnetic field of the MRI magnet is expressed as the sum of spherical harmonic terms, and the optimized current density of shim coils capable of removing higher-order terms is calculated by the Tikhonov regularization method. To investigate all potential designs derived from calculated current density, 4 sweeping parameters are selected: (1) axial length of shim coil zone; (2) radius of shim coils; (3) exact axial position of shim coils; and (4) operating current. After adequate designs are determined with constraints of critical current margin and homogeneity criterion, the total wire length required for each is calculated and the design with a minimum of them is chosen. Using the superconducting wire length of 9.77 km, the field homogeneity over 50 cm DSV is improved from 24 ppm to 1.87 ppm in the case study for 9.4 T whole-body MRI shimming. Finally, the results are compared with the finite element method (FEM) simulation results to validate the feasibility and accuracy of the design.