In order to study the propagation laws of acoustic wave of coal samples from the Upper Permian Xuanwei Formation in the east of Yunnan Province, China, under saturated water and dry conditions, the basic physical parameters, acoustic parameters and anisotropic parameters were obtained through the experiments. Based on FFT and wavelet analysis theory, the spectral characteristics of coal samples under different conditions were studied. The results show that physical parameters of coal samples in different directions have different values, that is, the anisotropy of coal samples is obvious. When the coal samples are saturated with water, the acoustic velocities and the attenuation coefficient increase, whereas the dominant frequency decreases. The signal amplitude of the frequency domain significantly decreases, that is, the internal structure of coal samples is damaged. The P-wave velocity and S-wave velocity increase with the increase of the confining pressure, whereas the anisotropy parameters decrease with the increase of the confining pressure. Overall, this study provides the basis to understand basic acoustic information and anisotropy characteristics of coal samples.