It is necessary to develop a high homogeneous, low power consumption, high frequency and small-size shim coil for high precision and low-cost atomic spin gyroscope (ASG). To provide the shim coil, a multi-objective optimization design method is proposed. All structural parameters including the wire diameter are optimized. In addition to the homogeneity, the size of optimized coil, especially the axial position and winding number, is restricted to develop the small-size shim coil with low power consumption. The 0-1 linear programming is adopted in the optimal model to conveniently describe winding distributions. The branch and bound algorithm is used to solve this model. Theoretical optimization results show that the homogeneity of the optimized shim coil is several orders of magnitudes better than the same-size solenoid. A simulation experiment is also conducted. Experimental results show that optimization results are verified, and power consumption of the optimized coil is about half of the solenoid when providing the same uniform magnetic field. This indicates that the proposed optimal method is feasible to develop shim coil for ASG.