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Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the structure of the lifted models using the traditional lifting technique. Furthermore, an auxiliary model-based multi-innovation stochastic gradient algorithm is presented to estimate the parameters involved in the linear and nonlinear blocks. The simulation results confirm that the proposed algorithm is effective and can achieve a high estimation performance.