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Many papers report the AC transport current loss characteristics in HTS coils, which occur because the HTS tapes in the coil transport a current in a magnetic field generated by the currents in adjacent tapes. We previously reported our experimental results on the loss from HTS tape in an AC and DC mixed electro-magnetic condition which consists of the DC offset transport current, AC transport current and AC magnetic field. Losses were measured in the same segment by the electric and calorimetric methods, and we established the possibility of measuring the loss using the electric method in the AC and DC mixed electro-magnetic condition. Now, we report the loss characteristics with AC and DC offset transport current in an HTS double pancake coil. We measured the AC and DC loss components by a four-terminal method. The voltage from the HTS coil includes the large AC inductive voltage, and we canceled the inductive voltage using a cancel coil placed in the center of the HTS coil. We report our findings on the loss characteristics in an HTS coil with AC and DC offset current in the HTS coil.