Recently, knowledge discovery in large data increases its importance in various fields. Especially, data mining from time-series data gains much attention. This paper studies the problem of finding frequent episodes appearing in a sequence of events. We propose an efficient depth-first search algorithm for mining frequent serial episodes in a given event sequence using the notion of right-minimal occurrences. Then, we present some techniques for speeding up the algorithm, namely, occurrence-deliver and tail-redundancy pruning. Finally, we ran experiments on real datasets to evaluate the usefulness of the proposed methods.