Mitochondria possess a remarkable ability to rapidly accumulate and sequester Ca2+. One of the mechanisms responsible for this ability is believed to be the rapid mode (RaM) of Ca2+ uptake. Despite the existence of many models of mitochondrial Ca2+ dynamics, very few consider RaM as a potential mechanism that regulates mitochondrial Ca2+ dynamics. To fill this gap, a novel mathematical model of the RaM mechanism is developed herein. The model is able to simulate the available experimental data of rapid Ca2+ uptake in isolated mitochondria from both chicken heart and rat liver tissues with good fidelity. The mechanism is based on Ca2+ binding to an external trigger site(s) and initiating a brief transient of high Ca2+ conductivity. It then quickly switches to an inhibited, zero-conductive state until the external Ca2+ level is dropped below a critical value (similar to 100-150 nM). RaM's Ca2+- and time-dependent properties make it a unique Ca2+ transporter that may be an important means by which mitochondria take up Ca2+ in situ and help enable mitochondria to decode cytosolic Ca2+ signals. Integrating the developed RaM model into existing models of mitochondrial Ca2+ dynamics will help elucidate the physiological role that this unique mechanism plays in mitochondrial Ca2+-homeostasis and bioenergetics.