The wavelet analysis method is introduced in this paper to study the nonstationary vibration of vehicles. A new road model, a so-called time domain correlated four-wheel road roughness, which considers the coherence relationships between the four wheels of a vehicle, has been newly developed. Based on a vehicle model with eight degrees of freedom, the analysis of nonstationary random vibration responses was carried out in a time domain on a computer. Verification of the simulation results show that the proposed road model is more accurate than previous ones and that the simulated responses are credible enough when compared with some references. Furthermore, by taking wavelet analysis on simulated signals, some substantial rules of vehicle nonstationary vibration, such as the relationship between each vibration level, and how the vibration energy flows on a time-frequency map, beyond those from conventional spectral analysis, were revealed, and these will be of much benefit to vehicle design.