The electrochemical organic memristor with polyaniline active layer is a stand-alone device designed and realized for reproduction of some synapse properties in the innovative electronic circuits, such as the new field-programmable gate arrays or the neuromorphic networks capable for learning. In this work a new theoretical model of the polyaniline memristor is presented. The developed model of organic memristor functioning was based on the detailed consideration of possible electrochemical processes occuring in the active zone of this device including the mass transfer step of ionic reactants. Results of the calculation have demonstrated not only the qualitative explanation of the characteristics observed in the experiment, but also quantitative similarities of the resultant current values. This model can establish a basis for the design and prediction of properties of more complicated circuits and systems (including stochastic ones) based on the organic memristive devices.