This paper presents a bio-inspired caterpillar-like climbing method. Natural caterpillars climb relatively slow, but their multisegmented body trunk strongly enhances climbing versatility and stability, which thus motivates us to design an imitative robot to study the caterpillar-like climbing locomotion. Based on observations from natural caterpillars, we propose a three-stage climbing method to imitate the caterpillar-like straight line climbing on a planar wall. Due to the redundancy property of caterpillars' multisegmented body trunk, we formulate the caterpillar-like climbing problem as an end-effector tracking problem using the redundant robotics terminology. A dual-mode optimal controller, which effectively resolves the end-effector tracking problem even when the robot configuration is ill-conditioned, is incorporated for realizing the caterpillar-like climbing locomotion. Both simulation and experiment results are presented to demonstrate the effectiveness of the proposed caterpillar-like climbing method.