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Two-dimensional polyimide covalent organic framework (2D PI-NT COF) films were constructed on indium tin oxide-coated glass substrates to fabricate two-terminal sandwiched resistive memory devices. The 2D PI-NT COF films condensated from the reaction between 4,4',4″-triaminotriphenylamine and naphthalene-1,4,5,8-tetracarboxylic dianhydride under solvothermal conditions demonstrated high crystallinity, good orientation preference, tunable thickness, and low surface roughness. The well-aligned electron-donor (triphenylamine unit) and -acceptor (naphthalene diimide unit) arrays rendered the 2D PI-NT COF films a promising candidate for electronic applications. The memory devices based on 2D PI-NT COF films exhibited a typical write-once-read-many-time resistive switching behavior under an operating voltage of +2.30 V on the positive scan and -2.64 V on the negative scan. A high ON/OFF current ratio (>106 for the positive scan and 104-106 for the negative scan) and long-term retention time indicated the high fidelity, low error, and high stability of the resistive memory devices. The memory behavior was attributed to an electric field-induced intramolecular charge transfer in an ordered donor-acceptor system, which provided the effective charge-transfer channels for injected charge carriers. This work represents the first example that explores the resistive memory properties of 2D PI-COF films, shedding light on the potential application of 2D COFs as information storage media.