To avoid the root lost problem in the former methods, a new method of solving the eigenproblem of Rayleigh wave in multilayered viscoelastic medium. The reason of root-lost and pseudo-root phenomenon is analyzed. From this, a series of different initial imaginary parts are employed, and the roots whose imaginary part is larger than real part are omitted. A flowchart of solving the eigenproblem is presented based on this, and the eigenproblem of Rayleigh wave in multilayered viscoelastic medium in an example is successfully solved with the method. The results show that there is no root-lost and pseudo-root phenomenon when solving the eigenproblem with the method. In the eigenproblem of Rayleigh wave in multilayered viscoelastic medium, root-lost and pseudo-root phenomenon can be avoided by employing a series of different initial imaginary parts and omitting the roots whose imaginary part is larger than real part.