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Vortex-induced vibration (VIV) is a typical nonlinear fluid-structure interaction phenomenon, which widely exists in practical engineering (the flexible riser, the bridge and the aircraft wing, etc). The conventional finite element model (FEM)-based and data-driven approaches for VIV analysis often suffer from the challenges of the computational cost and acquisition of datasets. This paper proposed a transfer learning enhanced the physics-informed neural network (PINN) model to study the VIV (2D). The physics-informed neural network, when used in conjunction with the transfer learning method, enhances learning efficiency and keeps predictability in the target task by common characteristics knowledge from the source model without requiring a huge quantity of datasets. The datasets obtained from VIV experiment are divided evenly two parts (source domain and target domain), to evaluate the performance of the model. The results show that the proposed method match closely with the results available in the literature using conventional PINN algorithms even though the quantity of datasets acquired in training model gradually becomes smaller. The application of the model can break the limitation of monitoring equipment and methods in the practical projects, and promote the in-depth study of VIV.