To further improve the filtering accuracy and robustness of generalized high-degree cubature Kalman filter when the random variable is with non-Gaussian distribution, a filtering algorithm named Huber-based robust generalized high-degree cubature Kalman filter algorithm is proposed. It is interpreted that the basic idea of the Huber method acting on the Kalman filter can be described as truncating the average from the perspective of recursive Bayesian approximation estimation. The observation vector is preprocessed by using the Huber method, and the normal measurement update is implemented, so that the robustness of the GHCKF algorithm is realized. The proposed method doesn't need approximating nonlinear measurements model by using the statistical linear regression model. The simulation results show that the proposed method has superior performance in robustness and estimation precision.