The IEEE 802.15.4 protocol is designed to flexibly support both real-time and contention-based services. When the beacon model is enabled, guaranteed time slot (GTS) scheduling can provide contention-free access to latency-sensitive services based on the time-division multiple-access mechanism. This characteristic makes IEEE 802.15.4 the appropriate candidate for vehicular sensor networks in which mobile nodes need to exchange packets with roadside units (RSUs) within a limited duration. In this paper, using network calculus theory, we analyzed the relationship between time-slot utilization and the corresponding access parameters, such as packet arrival rate, burst size, and vehicles' mobility extent. Then, for a given number of vehicles preparing to access an RSU, we proposed a time-sensitive weighted round-robin (TS-WRR) scheduler to improve the multiple-access performance, which can take the service delay requirement, packet arrival rate, and vehicular mobility level into account. Next, the weight determination and time-slot allocation strategy of the TS-WRR scheduler were issued in detail, which incorporate the special limitations and application requirements in a vehicle-to-infrastructure (V2I) communication environment. To make our model feasible for testing, we also elaborately demonstrated the implementation procedure with pseudocode and simulator design. Numerical results show that our TS-WRR scheduler outperforms some classic schedulers such as First-Come First-Served and WRR, as well as two latest works, i.e., implicit GTS allocation scheme and adaptive real-time GTS allocation mechanism in terms of delay guarantee and GTS utilization maximization in vehicular sensor networks.