With an increasing number of cloud service providers (CSPs), research works on multi-cloud environments to provide solutions to avoid vendor lock-in and deal with the single-point failure problem have expanded considerably. However, a few schemes focus on the conditional privacy protection authentication of vehicular networks under a multi-cloud environment. In this regard, we propose a robust and extensible authentication scheme for vehicular networks to fulfil the evergrowing diversified service demands from users. According to our solution, the vehicles need to register with the trusted authority (TA) only once to achieve a fast and efficient authentication with CSPs. Additionally, as long as the new CSP is successfully registered in TA, it can participate in vehicular service. A cloud broker, which is managed by the TA, is responsible for connecting all the cloud services; consequently, the complexity involved in the selection of CSPs is hidden from the users' view. A detailed security analysis establishes that our scheme can fulfil conditional privacy protection and achieve the security objectives of vehicular networks. Our scheme is based on elliptic curve cryptography and does not employ the complex bilinear pairing operation. An evaluation of performance of the proposed scheme indicates that it is suitable for applications involving vehicular networks.