The hardware circuit of neural network based on forgetting memristor not only has the characteristics of high computational efficiency and low power consumption, but also has the advantage that a memristor can store the weight of long-term memory and short-term memory. Neural networks based on forgetting memristors can process two different data sets, however, the number of data sets processed is determined by the conversion rate of short-time memory network to long-term memory network. In this paper, a model of forgetting memristor with controllable decay rate is proposed, the voltage source signal is used to set the weight and decay rate of long and short-term memory, and the hardware simulation circuit of long-term and short-term memory(LSTM) network was built based on the forgetting memristor bridge array, and tested on KMNIST and FASHION-MNIST data sets. The experimental results show that the long-term memory network and the short-term memory network can be converted into each other in the LSTM network based on