Unmanned underwater vehicle-dual-manipulator systems (UVDMSs) have attracted much research due to their humanoid operation capabilities, which have the advantage of cooperative manipulations and transporting underwater objects. Meanwhile, collision avoidance of UVDMSs is more challenging than that of unmanned underwater vehicle-dual manipulator systems (UVMSs). In this work, a model predictive control (MPC) approach is proposed for collision avoidance in objects transporting tasks of UVDMSs. The minimum distances of mutual manipulators and frame obstacles are handled as velocity constraints in the optimization of the UVDMS’s object tracking control. The command velocity generated by the model predictive kinematic controller is tracked by a dynamic inversion control scheme while model uncertainties are compensated by a neural network. Moreover, the tracking errors of the proposed dynamic controller are proved to be convergent by the Lyapunov method. At last, a three-dimensional (3D) UVDMS simulation platform is developed to verify the effectiveness of the proposed control strategy in the tasks of collision avoidance and object transport.