Considering the coupling of pitch and yaw motions as well as the cross-coupling of radome error, a multivariate simplification approach for stability analysis is proposed. Firstly, a guidance/control/missile multi-loop system (GCMMS) for a bank-to-turn missile with radome error is constructed. The simplified linear time-invariant (LTI) model of the GCMMS is established using the state-space model and small-perturbance linearization method. Then, based on the eigenvalue relative sensitivity matrix and system relative variation matrix, a multivariable simplification approach is proposed to analyze the stability of the GCMMS with radome error. Verification and analysis are conducted based on typical attack scenarios. The consistency between the analysis and the results of the nonlinear model verifies the effectiveness of the proposed approach. It indicates that the GCMMS has better tolerance for negative radome slope matrix, and the cross-coupling of the radome error cannot be ignored.