A connected vehicle (CV) environment is composed of a diverse data collection, data communication and dissemination, and computing infrastructure systems that are vulnerable to the same cyberattacks as all traditional computing environments. Cyberattacks can jeopardize the expected safety, mobility, energy, and environmental benefits from connected vehicle applications. As cyberattacks can lead to severe traffic incidents, it has become one of the primary concerns in connected vehicle applications. In this paper, we investigate the impact of cyberattacks on the vehicle-to-infrastructure (V2I) network from a V2I application point of view. Then, we develop a novel V2I cybersecurity architecture, named CVGuard, which can detect and prevent cyberattacks on the V2I environment. In designing CVGuard, key challenges, such as scalability, resiliency and future usability were considered. A case study using a distributed denial of service (DDoS) on a V2I application, i.e., the Stop Sign Gap Assist (SSGA) application, shows that CVGuard was effective in mitigating the adverse effects created by a DDoS attack. In our case study, because of the DDoS attack, conflicts between the minor and major road vehicles occurred in an unsignalized intersection, which could have caused potential crashes. A reduction of conflicts between vehicles occurred because CVGuard was in operation. The reduction of conflicts was compared based on the number of conflicts before and after the implementation and operation of the CVGuard security platform. Analysis revealed that the strategies adopted by the CVGuard were successful in reducing the inter-vehicle conflicts by 60% where a DDoS attack compromised the SSGA application at an unsignalized intersection.