Content dissemination in Vehicular Ad hoc Networks (VANET) is a challenging topic due to the high mobility of nodes, resulting in the difficulty of keeping routing tables updated. State-of-the-art proposals overcome this problem by avoiding the management of routing tables but resort to the so-called table of neighbors (NT) from which a next-hop is selected. However, NTs also require updating. For this purpose, some solutions resort to broadcasting beacons. We propose a Context- and Mobility-Aware Forwarding (CMAF) strategy that resorts to a Short-Term Mobility Prediction—STMP—algorithm, for keeping the NT updated. CMAF is based in Named Data Networking (NDN) and works in two modes, Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I). V2V CMAF leverages the overheard packets to extract mobility information used to manage NT and feed the STMP algorithm. V2I CMAF also uses a controlled and less frequent beaconing, initially from the Road-Side Units (RSUs), for a further refinement of the predictions from STMP. Results from extensive simulations show that CMAF presents superior performance when compared to the state of the art. In both modes, V2V and V2I (with one beacon broadcast every 10 s) present 5–10% higher Interest Satisfaction Ratio (ISR) than those of CCLF for the same overhead, at a cost of 1 s of increased Interest Satisfaction Delay (ISD). Moreover, the number of retransmissions of CMAF is also comparatively low for relatively the same number of hops. Compared to VNDN and Multicast, CMAF presents fewer retransmissions and 10% to 45% higher ISR with an increased overhead of about 20%.