Coal is a complex viscoelastic porous medium with fractal characteristics at different scales. To model the macroscale structure of coal, a fractal viscoelastic model is established, and the P-wave velocity dispersion and attenuation characteristics are discussed based on the complex modulus derived from this model. The numerical simulation results indicate that the fractional order and relaxation time greatly affect the P-wave velocity dispersion and attenuation. The fractal viscoelastic model indicates a full-band velocity dispersion between 1 Hz and 104 Hz. Meanwhile, the P-wave velocity has a weaker dispersion with the fractal viscoelastic model than with the Kelvin-Voigt model and Zener model between 1 Hz and 104 Hz for the same relaxation time and elastic modulus, but the velocity at 1 Hz based on the fractal viscoelastic model is higher with the Kelvin-Voigt model and Zener model. Simultaneously, the velocities of five coal samples are tested, and the attenuation factor is calculated using a low-frequency system. The experimental results indicate a strong dispersion in coal in the range of 10–250 Hz. The classic Kelvin-Voigt model and Zener model cannot describe the dispersion characteristics of coal, but the fractal viscoelastic model can describe them well by using the appropriate fractional order and relaxation time.