Mining sequential patterns for discovering frequent sequences has been widely studied as a data mining problem. A challenging research is to extend its use to data streams. A data steam is an unbounded, continuously generated sequence of data transactions. In this paper, we propose an online single-pass algorithm called OFSD (Online Frequent Sequence Discovery), to mine the set of all frequent sequences in a data stream whose frequency rates satisfy a minimum user defined frequency rate V;). The algorithm significantly reduces the number of elements in the candidate set (a set of candidate sequences that should be kept for further exploration) that efficiently increases its performance in comparison with other general solutions. The simulation results show the effects off; variation and the application defined threshold (C,) on the frequent phrase detection process.