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This paper reports on the current density and specific absorption rate (SAR) analysis of biological tissue surrounding an air-core transcutaneous transformer for an artificial heart. The electromagnetic field in the biological tissue is analyzed by the transmission line modeling method, and the current density and SAR as a function of frequency, output voltage, output power, and coil dimension are calculated. The biological tissue of the model has three layers including the skin, fat, and muscle. The results of simulation analysis show SARs to be very small at any given transmission conditions, about 2-14 mW/kg, compared to the basic restrictions of the International Commission on nonionizing radiation protection (ICNIRP; 2 W/kg), while the current density divided by the ICNIRP's basic restrictions gets smaller as the frequency rises and the output voltage falls. It is possible to transfer energy below the ICNIRP's basic restrictions when the frequency is over 250 kHz and the output voltage is under 24 V. Also, the parts of the biological tissue that maximized the current density differ by frequencies; in the low frequency is muscle and in the high frequency is skin. The boundary is in the vicinity of the frequency 600-1000 kHz.