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A vehicular ad hoc network (VANET) consists of vehicles, roadside units, and other infrastructures that communicate with each other with the goal of improving road safety, reducing accidents, and alleviating traffic congestion. For safe and secure operation of critical applications in VANET, it is essential to ensure that only authenticated vehicles can participate in the network. Another important requirement for VANET communication is that the privacy of vehicles and their users must be protected. Privacy can be improved by using pseudonyms instead of actual vehicle identities during communication. However, it is also necessary to ensure that these pseudonyms can be linked to the real vehicle identities if needed, in order to maintain accountability. In this paper, we propose a new blockchain-based decentralized pseudonym management scheme for VANET. This allows the vehicles to maintain conditional anonymity in the network. The blockchain is used to maintain a record of each vehicle and all of its pseudo-IDs. The information in the blockchain can only be accessed by authorized entities and is not available to all vehicles. The proposed distributed framework maintains an immutable record of the vehicle data, which is not vulnerable to a single point of failure. We compared the performance of the proposed approach with a traditional PKI scheme and shown that it significantly reduces the authentication delay.