Online, one-pass mining Web click streams poses some interesting computational issues, such as unbounded length of streaming data, possibly very fast arrival rate, and just one scan over previously arrived Web click-sequences. In this paper, we propose a new, single-pass algorithm, called DSM-TKP (Data Stream Mining for Top-K Path traversal patterns), for mining a set of top-k path traversal patterns, where k is the desired number of path traversal patterns to be mined. An effective summary data structure, called TKP-forest (a forest of Top-K Path traversal patterns), is used to maintain the essential information about the top-k path traversal patterns generated so far. Experimental studies show that the proposed DSM-TKP algorithm uses stable memory usage and makes only one pass over the streaming Web click-sequences.