To address the uneven seabed following control problem under the time delay constraint of the actuator for the autonomous underwater vehicle (AUV), a robust time-delay controller with prescribed performance guidance law is proposed in this paper, which can improve the safety of the AUV during navigation. First, the seabed following error conversion is firstly performed based on a navigational safety barrier function. Then, by integrating the time-varying line-of-sight guidance angle, the prescribed performance guidance law is designed at the kinematics level to provide reference state input for the AUV. After that, to tackle the time delay problem of actuators and reduce demand for accurate modeling, a robust time-delay dynamic controller is designed using the radial basis function (RBF) neural network. Finally, based on the Lyapunov theory, the stability of the closed-loop system is proved. The simulation results illustrate that the designed controller can achieve uneven seabed following control. Moreover, the following errors are always confined to the preset limits, which can also enhance the safety performance of the AUV when following the uneven terrain of the seabed.