In urban vehicular ad hoc networks (VANETs), due to the high mobility and uneven distribution of vehicles, how to select an optimal relaying node in an intra-street and how to determine a street selection at the intersection are two challenging issues in designing an efficient routing protocol in complex urban environments. In this paper, we build a link model with a Wiener process to predict the probability of link availability, which considers the stable and unstable vehicle states according to the behavior of vehicles. We introduce a novel concept called the link correlation which represents the influence of different link combinations in network topology to transmit a packet with less network resource consumption and higher goodput. Based on this concept, we design an opportunistic routing metric called the expected transmission cost over a multi-hop path (ETCoP) implemented with our link model as the selection guidance of a relaying node in intra-streets. This metric can also provide assistance for the next street selection at an intersection. Finally, we propose a street-centric opportunistic routing protocol based on ETCoP for VANETs (SRPE). Simulation results show that our proposed SRPE outperforms the conventional protocols in terms of packet delivery ratio, average end-to-end delay, and network yield.