The invention belongs to the technical field of information security, in particular to a strong physically unclonable function (PUF) circuit based on a memristor. The PUF circuit comprises a non-volatile storage array, a 2T2R basic unit, a row address generation module, a column address generation module, a comparison address generation module, a PUF column selector, a PUF row decoder, a comparison current column selection module, a reading and resetting module, a comparison and resetting module, a reading circuit module, a Mbit register and counter module and a multiple XOR module, wherein the address generation module is used for generating a row selection signal and a column selection signal; the PUF column selector is used for address decoding; the reading and resetting module is usedfor generating reading, writing and comparison signals; the reading circuit module is applied to a readout circuit; the Mbit register and counter module is used for temporary storage of results; and the multiple XOR module is used for enhancing anti-modeling attacks. The invention also provides a set of operation flow to improve the area utilization ratio and randomness of the strong PUF of the memristor. The memristor strong PUF circuit disclosed by the invention has the characteristics of high area utilization ratio, configurability, reusability, excellent randomness and anti-modeling attackability.