Trajectory similarity computation is an essential operation in many applications of spatial data analysis. In this paper, we study the problem of trajectory similarity computation over spatial network, where the real distances between objects are reflected by the network distance. Unlike previous studies which learn the representation of trajectories in Euclidean space, it requires to capture not only the sequence information of the trajectory but also the structure of spatial network. To this end, we propose GTS, a brand new framework that can jointly learn both factors so as to accurately compute the similarity. It first learns the representation of each point-of-interest (POI) in the road network along with the trajectory information. This is realized by incorporating the distances between POIs and trajectory in the random walk over the spatial network as well as the loss function. Then the trajectory representation is learned by a Graph Neural Network model to identify neighboring POIs within the same trajectory, together with an LSTM model to capture the sequence information in the trajectory. We conduct comprehensive evaluation on several real world datasets. The experimental results demonstrate that our model substantially outperforms all existing approaches.