As the basis of time series data mining tasks, such as indexing, clustering, classification, and anomaly detection, subsequence matching has been researched widely. Since the traditional time series subsequence matching only aims at matching the exactly same or approximately same patterns, a new sequence pattern with similar tendency, called time series homogeneous pattern, was defined. With mathematical derivation, the time series homogeneous pattern judgment rules were given, and an algorithm on time series homogeneous pattern discovery was proposed based on those rules. Firstly, the raw time series were preprocessed. Secondly, the homogeneous patterns were matched with segmentation and fitting subsequences. Since practical data can not satisfy the theoretical constraints, a parameter of homogeneous pattern tolerance was defined to make it possible for the practical data homogeneous patterns mining. The experimental results show that the proposed algorithm can effectively mine the time series homogeneous patterns.