The electrochemical organic memristive device with polyaniline active layer is a stand-alone device designed and realized for reproduction of some synapse properties in the innovative electronic circuits, including the neuromorphic networks capable for learning. In this work, a new theoretical model of the polyaniline memristive is presented. The developed model of organic memristive functioning was based on the detailed consideration of possible electrochemical processes occuring in the active zone of this device. Results of the calculation have demonstrated not only the qualitative explanation of the characteristics observed in the experiment but also the quantitative similarities of the resultant current values. It is shown how the memristive could behave at zero potential difference relative to the reference electrode. This improved 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.