Non-carrier-injection light-emitting diodes (NCI-LEDs) are expected to be widely used in the next-generation micro-display technologies, including Micro-LEDs and nano-pixel light-emitting displays due to their simple device structures. However, because there is no external charge carrier injection, the internal 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 in understanding its working mechanism and improving device performance. In this work, 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 bias and reverse bias of the internal PN junction increase with the driving frequency. When the driving frequency reaches a certain value, the forward bias and the reverse bias of the PN junction will 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 will always be in the state of exhaustion. According to the mathematical model, suggestions for the device optimization design are provided below. 1) Reducing the doping concentration of the induced charge region 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 the 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 e present a clear physical figure for understanding the working mechanism of NCI-LED, and to provide a theoretical guidance for optimizing the device structure.