Based on the classical HP memristor found by HP Lab, this paper presents an expanded model that making fully consideration of the influence of Ron, that is, Ron is the similar order of magnitude of Roff.Simulations proved that in some particular conditions, the hysteresis effect of the expanded model is the same as Hp memristor.A comparison was made between these two models under some given conditions.Then, we built several simulations to test the classical characteristics of the expanded HP memristor.Simulation results demonstrate that the expanded model is superior to the original in some aspects like easy switching and power saving.At last, we applied the expanded HP memristor in STDP learning simulation, which shows it is a good candidate for neural network when a threshold voltage function is proposed.