Trajectory synthesis with a series of fake locations has been deemed as a promising obfuscation technology to preserve the individual privacy of users in Location-Based Services (LBSs). However, a number of previous approaches fail to take into consideration the geographic distance and motion direction of the real locations to synthesize trajectories. As a result, most of them always cannot represent the statistical characteristics of real trajectories in a privacy-preserving manner, and thus suffer from various attacks through data analysis. To tackle this issue, this paper presents SPSD, a novel privacy-preserving trajectory synthesis approach with a$k$-anonymous guarantee, through extracting the semantic, geographic and directional similarity of locations from the real trajectories to create plausible trajectories. SPSD first classifies all historical trajectory data into a series of sets for location identity, by introducing the visiting time and visiting duration, which can clearly represent the semantic information of locations. Then,$4k$locations and$2k$of$4k$ones have been selected from each set to act as the initial disguises of each corresponding real location, with quantitative semantic and geographic similarities, respectively. In order to find enough fake locations for each real location in less time, the candidate locations have been narrowed down to$k$in direction recovery through step-by-step screening, with the$k$-anonymous property. Experiment results built on the real-world trajectory datasets indicate that SPSD has outperformed the previous approaches in terms of semantic similarity, directional accuracy and security resistance to synthesize privacy-preserving trajectories at the tolerable time cost.