The knowledge of Inter-vehicle link duration is an important parameter in Vehicular Ad hoc Networks (VANETs), as it is useful for vehicles to delay their information transmission if link breakage is anticipated before completing the transmission. In addition, it plays a pivotal role in routing, as it allows proactive construction of long-life paths, and optimizing next-hop selection in position-based routing (PBR). However, due to the high mobility of vehicles and the complicated vehicular mobility patterns in urban areas, the estimation of link duration in urban VANETs is still an open research issue. Different from other complex link duration estimation methods, we introduce a lightweight neural networks (NNs) based mobility prediction scheme which allows vehicles to autonomously predict their future mobility speed for a certain time window. Then, the expected speed is used in an urban area mobility prediction model to estimate link duration between neighbouring vehicles. Extensive simulation results are given to demonstrate the validity of the proposed methods.