Silicon oxide and silicon nitride are two key dielectrics in silicon devices. The advantage of Si3N4 over other dielectrics is that silicon nitride is compatible with silicon technology. It is required to study in detail the charge transport mechanism in a Si3N4-based memristor to further improve the cell element and to create a matrix of these elements. Despite many research activities carried out, the charge transport mechanism in Si3N4-based memristors is still unclear. Metal-nitride-oxide-silicon structures that exhibit memristor properties were obtained using low-pressure chemical vapor deposition at 700 °C. The fabricated metal-nitride-oxide-silicon memristor structure does not require a forming procedure. In addition, the metal-nitride-oxide-silicon memristor has a memory window of about five orders of magnitude. We found that the main charge transport mechanism in the metal-nitride-oxide-silicon memristor in a high resistive state is the model of space-charge-limited current with traps. In a low resistive state, the charge transport mechanism is described by the space-charge-limited current model with filled traps. Trap parameters were determined in the Si3N4-based memristor in the high resistive state.