As a typical data mining research topic, sequential pattern mining has been studied extensively for the past decade. Recently, mining various sequential patterns incrementally over stream data has raised great interest. Due to the challenges of mining stream data, many difficulties not so obvious in static data mining have to be reconsidered carefully. In this paper, we propose a novel algorithm which stores only frequent closed prefixes in its enumeration tree structure, used for mining and maintaining patterns in the current sliding window, to solve the frequent closed sequential pattern mining problem efficiently over stream data. Some effective search space pruning and pattern closure checking strategies have been also devised to accelerate the algorithm. Experimental results show that our algorithm outperforms other state-of-the-art algorithm significantly in both running time and memory use.