In vehicular ad hoc network (VANET), geographic routing protocols can preferably adapt to frequent topology changes and unstable link quality. Beacon messages are needed to share the positions of neighboring nodes, so forwarding decisions in the interval of successive beacon messages may be inaccurate due to the movement of the vehicle nodes. In this situation, trajectory prediction is needed to amend the positions of the vehicle nodes. Existing prediction algorithms are either lack of universality or suffered from large prediction errors. To solve the problems above, this paper proposes a new trajectory prediction algorithm, which is based on the measurement result that the vehicle accelerations obey normal distribution. The new algorithm uses linear regression to do the prediction and applies a feedback mechanism to amend error. The new trajectory prediction algorithm can greatly improve the prediction accuracy in several real trajectory trace tests. Then this paper proposes a new position based instant routing protocol. In instant routing protocol, a forwarder uses the predicted position of neighboring nodes and destination node to calculate the next hop. We apply our new trajectory prediction algorithm in instant routing to predict and update vehicle positions in real time. We use SUMO to generate real maps and vehicle trajectory traces, and use NS3 to do the simulation. Experimental results show that instant routing with the new trajectory prediction algorithm outperforms the traditional GPSR protocol and instant routing without trajectory prediction in terms of packet delivery ratio and network latency, while reducing protocol processing overhead remarkably.