Effective communication plays a vital role in the formation control of autonomous underwater vehicles (AUVs). However, the communication delay inherent in acoustic communication significantly impacts the performance of formations, especially when performing complex tasks or operations in dynamic marine environments. Therefore, this paper focuses on the affine formation control of multiple AUVs under acoustic communication delay. Firstly, to address the issues of communication delay caused by acoustic communication, a leader prediction compensation method based on the Interactive Multi-Model (IMM) algorithm is proposed. Then, a distributed affine formation control law based on the stress matrix is introduced. Finally, the effectiveness of the proposed method is validated through theoretical derivation and highfidelity numerical simulations.