As a special form of multiaccess edge computing (MEC), vehicular edge computing (VEC) plays an important role in emergency logistics by providing real-time and low-latency services for vehicles. The solution of the joint task offloading and resource allocation problem (JTORA) is the key to improving VEC efficiency. This study formulates a special model according to the multistage characteristics of the computational task in vehicular edge computing networks (VECNs) for emergency logistics. First, the JTORA problem is decomposed into three computational steps, each of which includes a task offload (TO) problem and a resource allocation (RA) problem. Then, a hybrid solution is proposed which uses a simulated annealing process to optimize the genetic algorithm (GA) and cooperate with the particle swarm optimization (PSO) algorithm, called the genetic simulated annealing and particle swarm optimization (GSA-PSO) algorithm. Furthermore, a simulation experiment is designed and the effectiveness of the GSA-PSO is verified.