Fast development of tracking devices has made trajectory outlier detection(TOD) possible and meaningful. Given a set of trajectories T, a TOD algorithm outputs a subset of T, of which trajectories are different from mostof the other trajectories in some aspect(s). These trajectories, namely outliers, can indicate important or interesting information and are thus worthnoticing. TOD techniques can be used for surveillance security, accidentdiscovery, and many other purposes. Many of the existing TOD algorithms consider only spatial trajectoryoutliers. They can detect trajectories that follow an abnormal route ordirection. While some existing algorithms are capable of detecting outliersin temporal aspects, like trajectories with abnormal time duration or speed,they have their own weaknesses. For example, they can be computationallyexpensive, or fail to detect important types of outliers. In this work, we aimto overcome these shortcomings of previous TOD algorithms. A novel grid-based TOD algorithm is proposed that is capable of detectingtemporal-spatial outliers including density, direction, duration, and speedoutliers with accuracy as well as fast calculation. The algorithm performsthe following three main steps: (i) it calculates density, direction, duration,and speed features of all trajectories in the input set T; (ii) it transformsfeature information of trajectories into grid information; (iii) it examineseach trajectory grid cell by grid cell. Following these three steps, outlyingtrajectories are extracted. By conducting experiments on several data setsincluding both simulated and real ones, the algorithm is shown to be efficientin detecting density, direction, duration, and speed outliers. It outperformsstate-of-the-art TOD algorithms in various aspects.