Focusing on the problem that the design of normal cubature Kalman filter(CKF) requires the precise statistical characters of the noise, an adaptive CKF is proposed. This algorithm can estimate and correct the statistical characters of the noise on-line by using Sage-Husa maximum a posterior(MAP) estimator in the filtering process therefore, and then can effectively improve the estimation accuracy and stability of the CKF. Considered in some cases, the noise covariance estimation will be abnormal and makes the filtering divergent, thus the corresponding remedy is proposed. The simulation results show that the adaptive CKF algorithm is feasible and effective, and it could obviously improve the filtering effect of normal CKF algorithm.