In this paper, we investigate noise covariance adaptive distributed Bayesian filter based on variational Bayesian inference method. In Bayesian filter framework, the joint distribution of state and noise covariance is approximated by variational distributions, where the unknown noise covariance is modeled by inverse-Wishart distribution. With communicating with neighbors, we show that the joint posterior distribution of state and noises can be approximated by recursively performing variational Bayesian expectation (VB-E) and variational Bayesian maximization (VB-M) steps. Then we use the cubature Kalman filter (CKF) to approximate Gaussian interval, and propose a variational Bayesian based distributed adaptive cubature information filter (VB-DACIF). Finally, we illustrate the effectiveness of the proposed estimation algorithm by a cooperative object tracking problem.