Because of wide range of applications, the flexible artificial synapse is an indispensable part for next-generation neural morphology computing. In this work, we demonstrate a flexible synaptic device based on a lift-off (In,Ga)N thin film successfully. The synaptic device can mimic the learning, forgetting, and relearning functions of biological synapses at both flat and bent states. Furthermore, the synaptic device can simulate the transition from short-term memory to long-term memory successfully under different bending conditions. With the high flexibility, the excitatory post-synaptic current of the bent device only shows a slight decrease, leading to the high stability. Based on the experimental conductance for long-term potentiation and depression, the simulated three-layer neural network can achieve a high recognition rate up to 90.2%, indicating that the system comprising of flexible synaptic devices could have a strong learning-memory capability. Therefore, this work has a great potential for the development of wearable intelligence devices and flexible neuromorphic systems.