In order to solve the task assignment problem of multiple heterogeneous autonomous underwater vehicle (AUV), a distributed robust auction algorithm is proposed. First, a heterogeneous multi-AUV task assignment distributed auction model is established, including the task assignment system (auctioneer) optimization model and the AUV optimization model. Second, in view of the existing auction algorithms that ignore the interests of the auctioneer and do not conform to the market rules, we introduce task reward feedback mechanism, and the task assignment system, through several rounds of testing the auction market, adaptively adjusts the task rewards, which effectively reduces the cost of task assignment system when guaranteeing AUV utility at the same time, for the purpose of promoting the task assignment system to participate in the auction. Finally, a robust optimization algorithm is proposed to deal with the uncertainties caused by underwater ocean currents, which improves the ability of multi-AUV task assignment system to deal with complex underwater environment. Simulation results show the robustness and effectiveness of the proposed algorithm.