Delay tolerant networks (DTNs) make use of opportunistic encounters of nodes for communication. The characteristics of high mobility of nodes, frequent link variation and long communication delays in DTNs result in an absence of an instantaneous end-to-end path from any source to a destination, making routing a challenge in DTNs. To deal with this issue, a lot of routing schemes have been proposed, in which future contacts of nodes are predicted based on node mobility traces and contact information. However, the previous works did not consider the spatial information of nodes, such as dwelling time at a location, and the transitivity of contacts in the prediction process of future encounter opportunities of nodes. In this paper, a novel mobility prediction-based routing (MPR) scheme is proposed for DTNs, in which the spatial information of nodes and contact transitivity are both taken into account. Specifically, a time-homogeneous semi-Markov process model is proposed to describe node mobility. By employing the semi-Markov model, we formulate the probability of a node destined to an area subject to the remaining time period constraint. The simulation results show that the proposed MPR scheme substantially improves delivery ratio and reduces delivery latency compared with traditional DTN routing schemes.