The dielectric spectroscopy of the ferroelectric liquid crystal mixture FLC-6980 doped with a low concentration (~2% wt/wt) of anthraquinone dye has been studied. The complex permittivity has been measured in the frequency range 100 Hz to 1 MHz in SmC^* and SmA phases. Dielectric increments and the relaxation frequencies at various temperatures have been evaluated. Our results indicate that the relaxation frequency and the SmC^*-SmA transition temperature T(C^*A) decreases whereas the dielectric increment increases about 2.5-fold on dye addition.