A tapered impedance-matching line is designed by an inverse scattering method for the one-dimensional medium. The phase compensation factor(PCF) is introduced in order to reduce the error in the inverse scattering process to reconstruct the permittivity profile. By estimating the permittivity profile of the virtual one-dimensional dielectric medium whose reflection characteristic is the same as that of the specified matching line, the matching line is synthesized. The method can be used to design impedance-matching lines with arbitrary passband characteristics without any equivalent circuit analysis. The inevitable errors in the method using the time-domain reflection coefficient can be avoided by using the frequency-domain reflection coefficient.