Destination prediction is very important in location-based services such as recommendation of targeted advertising location. Most current approaches always predict destination according to existing trip based on history trajectories. However, no existing work has considered the difference between the effects of passing-by locations and the destination in history trajectories, which seriously impacts the accuracy of predicted results as the destination can indicate the purpose of traveling. Meanwhile, the temporal information of history trajectories in destination prediction plays an important role. On one hand, the history trajectories in different periods also differ in the influence, e.g., the history trajectories from last week can reflect the status quo more accurately than the history trajectories two years ago. On the other hand, the history trajectories in different time slots reflect different facts of traffic and moving habits of people, e.g., visiting a restaurant in the daytime and visiting a bar at night. Although a huge amount of history trajectories can be achieved in the era of big data, it is still far from covering all the query trajectories since a road network is widely distributed and trajectory data is sparse. The temporal sensitivity of history trajectories highlights the sparsity problem even more. Therefore, we propose a novel model $\text{T-DesP}$ to solve the aforementioned problems. The model is comprised of two modules: trajectory learning and destination prediction. In the module of trajectory learning, a novel method called the mirror absorbing Markov chain model is proposed for modeling the trajectories for isolating the destination. We build a transition tensor to deduce the transition probability between each location pair in a particular time slot. To address the data sparsity problem, we fill the missing values in transition tensor through a context-aware tensor decomposition approach. In the module of destination prediction, an absorbing tensor is derived from the filled transition tensor, and the theoretical model is established for destination prediction. The experiments prove the effectiveness and efficiency of $\text{T-DesP}$.