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This paper investigates the delay sensitive secure transmission problem in unmanned aerial vehicle (UAV)-relayed vehicular ad hoc networks (VANETs). Specifically, we take the security assurance into account and formulate this problem as a total information delay minimization problem by optimizing the UAV relay trajectory and channel allocation. To tackle this optimization problem, we propose an alternating optimization framework, where the UAV relay trajectory is solved by the Newton method, and the channel allocation is obtained by relax-and-round and sequential convex approximation methods. Finally, simulation results show the performance improvement of our algorithm compared with the current works in terms of the total information delay. [ABSTRACT FROM AUTHOR]