Finite element analysis models were established for a rotary adapter by parameterizing the cross-section outlines. With the natural frequency and local maximum stress as constraints, lightweight optimization design of the adapter plate was carried out. Based on the amount of variables and high calculation cost of the optimization model, the radial basis function surrogate model taking in account spatial constraints was combined with global random optimization algorithm. Results show that the fitting errors of the first natural frequency and local maximum stress of the adapter meet the requirements of allowable values, and the fitting R2 values are 0.979 and 0.938 respectively. The relative deviations between the predicted value of frequency and stress of the optimized solution and the true value at different speeds are less than 10%, and the maximum absolute deviation values are 35.2Hz and 16.2MPa, respectively. The optimization process adopted can be effectively used for the design of the adapter.