We report on a new method for measuring the wavelength dependence of the complex permittivity of a thin gold film of a surface plasmon resonance (SPR) structure comprising a gold-coated SF10 slide with an adhesion film of chromium attached to an SF10 glass prism. The method is based on spectral interferometry and utilizes a setup with a birefringent crystal and the SPR structure in the Kretschmann configuration, in which channeled spectra are recorded and from them, the phase functions of the SPR for air at different angles of incidence are retrieved. The SPR phenomenon is manifested as an abrupt phase change with respect to the reference phase difference for the interference resolved with the SF10 glass prism alone. The phase changes for different angles of incidence are processed in the vicinity of the resonance wavelengths to obtain the real and imaginary parts of the complex permittivity in a wavelength range from 530 to 850 nm or equivalently, the parameters of a modified Drude-Lorentz model. This research, to the best of the authors' knowledge, is the first demonstration of spectral interferometry-based measurement of the complex permittivity function of a thin metal film, which is important from the point of view of material characterization directly performed in the Kretschmann configuration. The performance of the SPR sensor is strongly influenced by the choice of a thin metal film so it is crucial to know the complex permittivity function of the metal. Standard techniques to characterize thin metal films include spectral ellipsometry [15][16][17] and spectral reflectometry [18].