In order to solve the problem of computing resource management in the vehicle edge computing system, a computational offloading and resource allocation scheme based on Lyapunov stochastic optimization is proposed. This paper constructs the optimization problem of minimizing the service delay of vehicle users under the constraints of guaranteed task load and long-term energy consumption, and uses the Lyapunov stochastic optimization theory to decompose the optimization problem. In the local computing resource allocation sub-problem, the optimal local computing CPU frequency is obtained by solving the linear problem; in the computing offloading sub-problem, the optimal transmit power is obtained by numerical optimization. Finally, with the help of the drift penalty method in Lyapunov stochastic optimization, a low-complexity joint computing offloading and resource allocation algorithm is designed. The entire vehicle is realized by simultaneously controlling offloading decision-making, locally calculating CPU frequency, and calculating offloading transmit power. The service delay of vehicle users in the edge computing system is the smallest, which improves the service quality of vehicle edge computing. The simulation results verify the effectiveness of the proposed algorithm.