With the development of microelectronics and sensor technologies, implantable electronic devices are employed in many applications. These devices are distributed on or in the human bodies and are used to transmit signals wirelessly to external equipment. In conventional wireless communications, the antennas need a lot of space and power, and their strong electromagnetic interference limits the available locations for implantable devices. In the more recently developed galvanic coupling intra-body communication technology, human tissues are used as the media of signal transmission, and this method has therefore been applied to resolve the spatial limitations of conventional wireless communications methods. This paper presents a mathematical model of multi-layer galvanic coupling based on the volume conductor theory to analyze the transmission mechanism of these implantable intra-body communication devices. The proposed model is based on the quasi-static approximation conditions of Maxwell's equations, the field and potential are solved from Poisson's equation, and an equation was obtained to model the channel attenuation. The channel gain in a model of human limbs can be used to calculate within the frequency range of lesser than 1 MHz. To verify the accuracy and applicability of the model, the computed results were compared with the physiological saline and porcine tissue experimental results in the 100-kHz frequency.