The geometric form of upward and downward trends in time series was studied by analyzing the geometric characteristics of time series. Concepts of high or low filtering points and high or low filtering lines were proposed according to the variation characteristics of time series. These concepts were used to judge the upward trends and the downward trends of the time series. Furthermore, a piecewise linear representation of time series based on upward or downward property was proposed. The results of experiments show that this method is easy to be programmed. It has desirable approximation, runs fast, and keeps the shape of time series. Furthermore, the number of lines is small.