We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter. The natural gradient approach is applied to the Kullback-Leibler divergence between the parameterized variational distribution and the posterior density of interest. Using a Gaussian assumption for the parametrized variational distribution, we obtain a closed-form iterative procedure for the Kullback-Leibler divergence minimization, producing estimates of the variational hyper-parameters of state estimation and the associated error covariance. Simulation results in both a Doppler radar tracking scenario and a bearing-only tracking scenario are presented, showing that the proposed natural gradient method outperforms existing methods which are based on other linearization techniques in terms of tracking accuracy.