A common way to store information of spatio-temporal moving objects is to display the path of the objects as the form of a three-dimensional trajectory using the geographic location and time. In recent years, extensive research has been done on the trajectories. These studies have focused mainly on geometric aspects of trajectories. However, semantic trajectory is a relatively new concept that has been developed with the purpose of effective semantic analysis on captured data. In semantic trajectory, which is a secondary display of geometric trajectory, the movement of object is described as series of stop-and-move. Production of semantic trajectory from the collected raw data is a process with several steps. Due to the huge amount of data, one of the important processes is reducing the number of points of trajectory with maintaining the required accuracy by using compression techniques. However, data reduction techniques commonly are based on linear simplification and are not able to protect stop and move of trajectories. In this paper, a data reduction technique is presented which is based on combination of two distance functions for approximation of semantic trajectory. The first distance function has used speed of points to calculate the approximation error of trajectories. The second function is based on the development of well-known Douglas-Peuker algorithm, which assumes constant acceleration to calculate the approximation error. The proposed algorithm is implemented on real trajectory data and the results show improved performance compared with other algorithms in preservation of the stop and move of trajectories.