The trajectory planning of the arm is greatly facilitated by the physical direct teaching technology. Variable admittance control is a promising technology when a robot is interacting with a variable environment, such as a human whose stiffness might change during the interaction. Nevertheless, a canonical admittance controller with imperfect parameters may lead to robot oscillation, which brings more challenges to a variable admittance controller. In this paper, we propose an energy-based variable admittance controller with intrinsic oscillation suppression property. During the physical human–robot interaction (pHRI), the human intention is predicted based on the robot’s state and interaction force. The admittance parameters are tuned automatically to conform the robot’s motion to human intention. When the oscillation is detected online by the proposed wavelet module, our variable admittance model reveals oscillation suppression ability because of dissipating the energy generated by high-frequency oscillation. We compared the proposed variable admittance controller with other admittance controller approaches in both simulation and actual robot experiments. The proposed method shows significant improvement in oscillation suppression and human energy conservation in the human–robot interaction application.