Routing security has been paid more attention gradually in Vehicular Ad hoc Networks (VANETs). However, most existing routing protocols just focus on the behavior credibility which is a kind of subjective trust, merely applied to trust evaluation among familiar nodes, and cannot objectively reflect the trust degree of a given node in the whole network. So based on the former GPSR (Greedy Perimeter Stateless Routing) protocol, the concept of experiential trustiness is introduced as the metrics of credibility. We can establish trust relationships among strangers via extending GPSR protocol, and produce a novel trust routing protocols adaptive to the VANETs. According to the experiential trustiness we design a new dynamic packet forwarding rule, and give some recommendatory methods for calculating the experiential trustiness. The experimental results show that the proposed experiential trustiness is feasible and effective for trust evaluation among strangers. And in consideration of behavior trustiness on packet delivery ratio and routing packet transmission ratio indexes, the improved GPSR protocol(E-GPSR) has obvious advantages compared with the standard GPSR and the variant GPSR even when there are 50% selfish nodes in network. Moreover the improved GPSR also overmatches the other two protocols at throughput aspect in the case without malicious nodes.