A low-complexity Kalman-filter-based channel estimation method for orthogonal frequency-division multiplexing systems is proposed. This method belongs to the pilot-symbol-aided parametric channel estimation method in which the channel responses are characterised as a collection of sparse propagation paths. Because of the slow variation of the signal subspace in the channel samples' correlation matrix, the estimation of channel parameters is translated into an unconstrained minimisation problem. Then, in order to solve this optimisation problem, a subspace tracking by Kalman filter is carried out, which is characterised in that the state equation and the measurement equation are constructed upon the constant signal subspace. Further, this Kalman-filter-based method is extended to the multi-antenna scenarios efficiently. Simulation results show that the proposal can effectively track the time variations in both the block fading channels and the Doppler frequency spread channels.