Nonstoichiometric silicon nitride SiNx is a promising material for developing a new generation of high-speed, reliable flash memory device based on the resistive effect. The advantage of silicon nitride over other dielectrics is its compatibility with the silicon technology. In the present work, a silicon nitride-based memristor deposited by the plasma-enhanced chemical vapor deposition method was studied. To develop a memristor based on silicon nitride, it is necessary to understand the charge transport mechanisms in all states. In the present work, it was established that the charge transport in high-resistance states is not described by the Frenkel effect model of Coulomb isolated trap ionization, Hill–Adachi model of overlapping Coulomb potentials, Makram–Ebeid and Lannoo model of multiphonon isolated trap ionization, Nasyrov–Gritsenko model of phonon-assisted tunneling between traps, Shklovskii–Efros percolation model, Schottky model and the thermally assisted tunneling mechanisms. It is established that, in the initial state, low-resistance state, intermediate-resistance state and high-resistance state, the charge transport in the forming-free SiNx-based memristor is described by the space charge limited current model. The trap parameters responsible for the charge transport in various memristor states are determined.