Chaotic vibration has become increasingly popular in the study of acoustic and vibration engineering. Many engineering designs have taken advantage of the special characteristics of chaos, and deliberately introduced it into the system to improve efficiency. As an important component, leaf springs have long been used in the suspension system of wheeled vehicles. Recent development is considering chaotic vibration in the design of leaf springs to improve the system’s reliability. However, little experimental research has been carried out to investigate the chaos characteristics of leaf springs. Meanwhile, a preliminary study showed that some of the conventional signal processing methods may not be able to successfully identify the chaos features from a leaf spring test rig due to the complexity of the practical signal. Therefore, in this paper, a leaf spring system’s chaotic vibration and relevant signal processing strategy were investigated in theory and experiment. Firstly, the relationship between the amplitude and frequency of the double potential well system is derived with averaging method. The stability is analyzed on the Vander pol plane and the global bifurcation diagram and Lyapunov exponent spectrum are applied to determine the chaotic regime accurately. Numerical simulation was conducted using a finite element method to give an idea of the leaf spring’s natural frequencies where chaotic vibration can be potentially generated. The experimental rig was then designed based on double potential well theory to generate stable and repeatable chaotic vibration, and an experimental study was carried out to investigate the system’s response characteristics under different excitation strengths and frequencies. An improved signal processing method, Wavelet-SG-EEMD (Wavelet, Savitzky-Golay (SG) and Ensemble Empirical Mode Decomposition (EEMD)), was used to reduce noise and beneficial to identify chaotic features of the vibration signal generated by the system. The nonlinear vibration response features of the system were carefully analyzed. Sub-harmonic phenomena, periodic modes and chaotic behavior were discovered during the experiment.