Non-carrier-injection light-emitting diodes (NCI-LEDs) are expected to be widely used in next generation micro-display technologies, including Micro-LEDs and nano-pixel light-emitting displays due to their simple device structure. However, because there is no charge carrier injection from external electrodes, carrier transport behavior of the NCI-LED cannot be described by using the traditional PN junction and LED theory. Therefore, establishing a carrier-transport model for the NCI-LED is of great significance for understanding its working mechanism and for improving device performance. In this paper, carrier transport mathematical model of the NCI-LED is established and the mechanical behavior of charge-carrier transport is analyzed quantitatively. Based on the mathematical model, the working mechanism of the NCI-LED is explained, the carrier transport characteristics of the device are obtained. Additionally, the key features, including the length of the induced charge region, the forward biased voltage across the internal PN junction, and the reverse biased voltage across the internal PN junction are studied. Their relationships with the applied frequency of the applied driving voltage are revealed. It is found that both the forward and reverse biases of the internal PN junction increase with the driving frequency. When the driving frequency reaches a certain value, the forward and reverse bias of the PN junction would be maintained at a maximum value. Moreover, the length of the induced charge region decreases with the increase of the driving frequency, and when the frequency reaches a certain value, the induced charge region would always be in the state of exhaustion. According to the mathematical model, suggestions for the device optimization design are provided: (1) Reducing the doping concentration of the induced charge regions can effectively increase the voltage drop across the internal LED; (2) Employing the tunneling effect occurring in the reverse-biased PN junction can effectively improve the electroluminescence intensity; (3) Using square-wave driving voltage can obtain a larger voltage drop across the internal LED and increase the electroluminescence intensity. This work on the carrier transport model is expected to provide a clear physical image for understanding the working mechanism of NCI-LED, and to provide a theoretical guidance for optimizing the device structure.