Many kinds of peg-in-hole assembly strategies for an industrial robot have been reported in recent years. Most of these strategies are realized by utilizing visual and force sensors to assist robots. However, complex control algorithms that are based on visual and force sensors will reduce the assembly efficiency of a robot. This issue is thoughtless in traditional assembly strategies but is critical to further improve the efficiency of assembly automation. In this work, a new assembly strategy that is based on a displacement sensor and a variable compliant center is proposed to improve robot performance in assembly tasks. First, an elastic displacement device for this assembly strategy is designed, and its performance is analyzed. The displacement signal generated by the displacement sensor is used to detect the contact state of the peg and hole and to guide the robot to adjust the posture. Second, an assembly strategy, including the advantages of passive compliance and active compliance, and a simple assembly control system are designed to improve the assembly efficiency. Last, the effectiveness of the proposed assembly method is experimentally verified using a robot with 6 degrees of freedom and a chamferless peg and hole with a small clearance (0.1 mm). The experimental results show that the assembly strategy can successfully complete the precision peg-in-hole assembly and assist the robot in accurate assembly in industrial applications.