The mining of closed sequential patterns has attracted researchers for its capability of using compact results to preserving the same expressive power as traditional mining. Many studies have shown that constraints are essential for applications of sequential patterns. However, time constraints have not been incorporated into closed sequence mining yet. Therefore, we propose an algorithm called CTSP for closed sequential pattern mining with time constraints. CTSP loads the database into memory and constructs time-indexes to facilitate both pattern mining and closure checking, within the patterngrowth framework. The index sets are utilized to efficiently mine the patterns without generating any candidate or sub-database. The bidirectional closure checking strategy further speeds up the mining. The comprehensive experiments with both synthetic and real datasets show that CTSP efficiently mines closed sequential patterns satisfying the time constraints, and has good linear scalability with respect to the database size.