The Kalman filter(KF) is widely used for state estimation of linear systems. However, it requires accurate statistic of process noise, which is not plausible in practical applications. In this paper, an adaptive KF algorithm with recursive process noise estimation is constructed firstly by utilizing the covariance matching principle. Then, in order to break through the limitation of the KF that can only deal with the estimation problem of linear systems, the recursive process noise estimation is introduced into the ensemble Kalman filter(EnKF), so that an adaptive EnKF algorithm is proposed. Finally, the stability of the novel algorithm is proved through the estimation theory. Under the condition of unknown process noise statistic, the proposed adaptive EnKF algorithm still converges, moreover its filtering precision and stability are better than those of the standard EnKF. Simulation results validate the effectiveness of the presented algorithm.