Liquid crystals are useful for a wide range of applications due to their exceptional properties. Doping of liquid crystals with carbon nanotubes (CNTs), even at very low concentrations, produces a detectable effect on the liquid crystal (LC) properties that can be very attractive for various functions. In this study, an attempt was made to investigate the effect of CNTs on the electrical properties of a short-pitch and high-spontaneous-polarization ferro-electric LC mixture, FLC-6304, at different temperatures. The inclusion of the CNTs significantly reduced the polarization at temperatures well within the $SmC^*$ phase, but the effect was gradually reversed as the transition temperature was approached. The insertion of the CNTs also reduced the response time and the rotational viscosity of the FLC mixture, which is highly desirable in the LCD industry.