A strong tracking cubature Kalman filter based on variational Bayesian inference is proposed in order to handle the problem of the nonlinear system with model errors and time-varying noise. By using the fictitious noise compensating technique, the model errors are compensated. The fictitious noise is built by assuming the non-zero mean of noise is Gaussian, and its covariance belongs to the inverse Gamma distribution. The parameter of fictitious noise is estimated by the variational Bayesian inference and the state is estimated by using the strong tracking cubature Kalman filter. The simulation results show that the proposed algorithm can achieve better accuracy and robustness than the adaptive algorithm for the nonlinear system with model errors and time-varying noise.