Independent component analysis (ICA) has become a hotspot in signal processing area, and its computation algorithms and application are widely studied recently. In this paper, a sliding window ICA algorithm is studied to deal with time variant mixing model that the traditional ICA algorithms fail to work. For solving the problem caused by the indeterminacy of ICs in applying sliding window ICA algorithm, the value of kurtosis is employed as the index to sort the independent components at each window position. This idea is proved to be effective in most cases. In addition, a recursive learning rule of separation matrix based on sliding window is given, which can reduce the computation load of the algorithm obviously. The selection of window length is also discussed in this paper. Furthermore, the separation performance of the proposed algorithm are compared with the batch ICA algorithm. Experiment results show that the proposed algorithm can work well in the time variant mixing model and can be used for online blind source separation and dynamic independent component analysis.