The piecewise linear representation algorithm of the time series represents the whole series with fewer points according to trend changes in the series. However, most of these algorithms focus on the information of local sequence points and rarely pay attention to global data. Some algorithms only focus on fitting on datasets instead of being applied to classification. To solve these problems, this study proposes an algorithm for extracting trend features from time series based on angle key points and inflection points. The algorithm selects angle key points according to the angle change values of the sequence data and then extracts inflection points based on these key points. It determines whether interpolation is needed according to segmentation requirements, so as to obtain a segmentation sequence meeting the requirements. Fitting and classification experiments are conducted on simulated data and 40 public datasets. Experimental results show that the proposed algorithm exhibits better fitting on the simulated data, compared with other algorithms such as piecewise aggregate approximation (PAA), the TD algorithm, the BU algorithm, the FFTO algorithm based on inflection points, the Trend algorithm based on turning points and trend segments, and the ITTP algorithm based on trend turning points. On the UCR public datasets, the proposed algorithm achieves an average fitting error of 1.165. Its classification accuracy is 2.8% higher than the DTW-1NN algorithm published by Keogh.