Existing works have paid little attention to load balancing for deep neural network (DNN) inference by joint model deployment and task offloading in VEC. Thus, this paper focuses on load balancing with full consideration of characteristics for VEC and DNN inference tasks to improve quality of service. An optimization problem is formulated with the objective of minimizing the maximum load of roadside units (RSUs) under the constraints of per task response time, per task inference accuracy, etc. To solve the problem, a two-stage optimization algorithm is proposed. Specifically, for the first stage, a load-aware matching strategy is developed by deploying DNN models and offloading inference tasks. For the second stage, a strategy is designed by offloading DNN inference task between computation units, i.e., CPU and GPU in this paper, in each RSU to further achieve the load balancing in VEC. The simulations are conducted based on three kinds of DNN inference tasks, three different accuracy models for each kind, and four kinds of computation units. Simulations results show that, the proposed algorithm outperforms the state-of-the-art methods in terms of the maximum load in VEC. For example, the proposed algorithm can significantly decrease the maximum load by at least 42.9 \(\%\) for different numbers of RSUs, compared with two state-of-the-art methods.