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.