Subsequence matching algorithms have many applications on time-series, such as detecting specific patterns on Electrocardiogram (ECG) and temperature data. To the best of author's knowledge, there are relatively few research studies on time-series fuzzy subsequence matching yet, which better expresses the logic in real life compared to exact subsequence matching. In this paper, we firstly propose Naive Fuzzy Subsequence Matching based on Euclidean Distance (NFSM-ED) and Dynamic Time Warping (NFSM-DTW) for solving fuzzy subsequence matching problem on time-series, which can be treated as a basic benchmark of efficiency and accuracy. Then we extend it to a novel approach called UCR Fuzzy Subsequence Matching (UFSM) algorithm, which is inspired by UCRSuite. Finally, we develop it to Improved Fuzzy Subsequence Matching by kd-tree (IFSM-kd) and R*-tree (IFSM-R*), which can efficiently and effectively perform fuzzy subsequence matching on time-series. Additionally, the experiment results show that IFSM-R* and IFSM-kd are much faster than NFSM-ED, NFSM-DTW and UFSM with nearly no extra memory space required. Furthermore, IFSM-R* supports inserting and deleting indexes compared to IFSM-kd.