The 3rd Generation Partnership Project, Long Term Evolution (LTE) has recently completed its specifications for connected vehicular (V2X) service. In the meantime, researchers in academia and industry are addressing its security issues involving applications, network, and medium access control (MAC) layer protocols. However, the security issue in regard to resource allocation has never been considered until now. Especially in LTE PC5 link, resource allocation with a regular pattern (semi-persistence) to deliver V2X periodic messages may leak the location privacy, even when the other protocol layers are tightly secured. In this proposed paper, we provide a secure resource allocation strategy where the vehicular users employ different resource allocation approaches to various types of message deliveries to preserve their privacy. Specifically, the emergency message delivery, being the most time critical and occurring in random time, is provisioned using PC5 autonomous resource allocation (ARA) to protect the privacy. To curtail the collision, we propose a novel ARA approach called random access with status feedback (RASFB) based on Rel. 12 mode 2. The performance analysis shows the higher performance of the proposed RASFB when compared with the Rel. 12 and Rel. 14 without sacrificing security.