To obtain a time scale with better stability and robustness, integrating atomic clock ensemble is a common approach. As a celebrated optimal estimator, the Kalman filter (KF) can be employed to construct time-scale algorithms for atomic clock ensemble to generate a time scale. The original KF time-scale algorithm typically sets a priori measurement noise covariance matrix which kept constant throughout the operation process. However, practical measuring equipment would introduce non-stationary noise, causing the mismatch of noise covariance matrices and corrupting the stability of the generated time scale. To address this problem, a variational Bayesian adaptive Kalman filter (VB-AKF) time-scale algorithm is proposed for estimating the variance matrix of non-stationary noise in real time and improving the stability of time scale. As shown through the simulation that the proposed VB-AKF time-scale algorithm can quickly track the measurement noise variance and conquer the corruption due to the mismatch of noise covariance matrices. Under the same noise circumstance, the stability of time scale can be improved from \(5.42\times 10^{-12}@1s\) to \(1.46\times 10^{-12}@1s\) and from \(4.87\times 10^{-12}@1s\) to \(2.82\times 10^{-12}@1s\) by VB-AKF in set scenarios of clock ensemble respectively, achieving the equivalent stability as KF with priori true noise covariance matrix. Compared with the KF, the VB-AKF time-scale algorithm is better at handling the impact of non-stationary measurement noise on the stability of time scale.