Abstract: Objectives For the sake of improving the ability of the autonomous underwater vehicle (AUV) formation to perform tasks in complex obstacles scenarios, a distributed three-dimensional affine formation shape maneuver control method is proposed for the multi-AUVs formation. Methods Based on affine transformation theory and stress matrix, AUV formation shape can achieve the rotation, scaling, shear, coplanarity, collineation or their combination. Formation maneuver information is only determined by the leader AUVs, and the follower AUVs only needs to track their individual desired trajectory affinely localized by the leader AUVs. Meanwhile, the yaw consistency of multi-AUVs formation is achieved based on the Laplacian matrix. Furthermore, a non-singular integral terminal sliding mode controller is employed to ensure that the multi-AUVs formation can track the desired trajectory fast and with high accuracy. Results Through the high-fidelity simulation experiments, the proposed AUV formation maneuver control method can drive the multi-AUVs formation to realize the high-precision maneuvering transformation of three-dimensional formation, and has high maneuverability and strong robustness. Conclusions The proposed method enables the multi-AUVs formation to avoid complex underwater obstacles by flexible maneuvering formation, which improves the safety of AUV formation and the ability to perform tasks.