Molten salts in the sodium fluoride-calcium fluoride-barium fluoride-aluminum fluoride quaternary system are known as Hurter's bath and Sumitomo's bath for electrolytic refining of aluminum. The specific electrical conductivities of this quaternary molten salt system have been measured. 1) The specific conductivities of NaF-AlF_3 binary molten salts are found to be 5.17~2.33 ohm^ cm^ up to the composition range of 50 wt.% AlF_3 at 1000℃, and these values agree fairly well with the values reported in other works. 2) In these quaternary molten salts, the measured values of specific conductivity are 4.13~0.73 ohm^ cm^ in the composition range of 5~20 wt.% CaF_2 and 30~50 wt.% BaF_2 at 950℃. 3) When the weight percent of added CaF_2 and BaF_2 is kept constant, the specific conductivities of this quaternary molten salt system decrease almost linearly with an increase in AlF_3 content. Similarly, the values decrease with increase in the contents of CaF and BaF_2 4) In this quaternary molten salt system, such compounds as Na_3AlF_6, NaAlF_4, Na_5 Al_3F_ NaCaAlF_6 NaBaAlF_6, CaAlF_5 and BaAlF_5 are formed and several complex ions including AlF_6^ and AlF_4^- are considered to exist. The structures of the molten state are not clearly known. The validity law in the electrical conductivity by each component are questioned. 5) The specific conductivities of Hurter's and Sumitomo's baths have been measured at 750~950℃ as 0.96~1.25 ohm^ cm^ and 0.87~1.10 ohm^ cm^, respectively. 6) Experimental evidence shows the possibility that some other composition range in this quaternary system can be used as an electrolyte of aluminum refining, besides Hurter's or Sumitomo's bath.