Abstract: Viscoelastic materials are widely used for noise reduction, vibration reduction or noise elimination of underwater vehicles. With the development of numerical simulation techniques, the demand of accurately obtaining their dynamic parameters increases rapidly. Aiming at the acoustic tube measurement method, a fast inversion method of complex longitudinal wave velocity of viscoelastic materials based on complex reflection coefficient is proposed in this paper. By introducing the multi-modal decomposition method, the complex plane root search problem of complex longitudinal wave number transcendental equations is transformed into eigenvalue decomposition problem of expansion coefficient system matrix, and the expansion coefficient system matrix under three typical backing situations is derived. The influences of the multi-modal expansion truncation order and the measurement error of complex reflection coefficient on the accuracy of complex longitudinal wave velocity inversion are analyzed. Numerical simulations show that this method can quickly and accurately invert the complex longitudinal wave velocity of viscoelastic materials.