As one of the important tools for exploring the ocean, multiple autonomous underwater vehicles (multi-AUVs) system can complete complex tasks in complex Internet of Underwater Things. Collaborative target search, as a typical application of multiple autonomous underwater vehicle (AUV) systems, has been applied in the fields of territorial sea security and marine biology research. Among them, hunting task allocation is a key issue determining the effective application of multiple AUV systems. Therefore, this article proposes a hunting task assignment framework based on contract network (CN) to assign hunting tasks. In the investigated framework, the tenderee AUV (TAUV) is responsible for setting the task reward and assigning hunting tasks, while bidder AUVs (BAUVs) set the working time as bidding information. Combining the mobile energy consumption and communication energy consumption of hunter AUVs, we establish the revenue optimization model of BAUVs and the TAUV. Based on the above model, we model the interaction process of hunting task allocation process between BAUVs and the TAUV as a Stackelberg game, and use the backward induction method to prove that there is a unique Stackelberg equilibrium (SE) in the game. In addition, this article proposes a strategy search algorithm based on the steepest descent method (SSA_SDM) to obtain the optimal strategy of BAUVs and the TAUV, which can achieve SE. Finally, experimental results show that SSA_SDM can reach the SE and outperform other algorithms.