Based on Navier-Stokes (N-S) equations, the numerical simulation of computational fluid dynamics (CFD) is one of the commonly used methods to investigate unsteady periodic fluid flow. However, it requires a calculation process that consumes a lot of time. To address the high time cost of N-S equation, an unsteady periodic fluid flow prediction framework is proposed in this study based on graph convolution recurrent network. It enables the fast prediction of fluid flow state. Herein, with the historical data of fluid flow as input, the physical model of the fluid is constructed through the graph convolution recurrent network to predict the fluid flow state. The results show that this prediction model based on graph convolution recurrent network is applicable to accurately predict the hydrodynamic laws, with an excellent performance achieved in predicting various flow field variables such as velocity, vortex, pressure etc. Compared with the traditional method to solve N-S equation, the graph convolution recurrent network shows an improvement by more than 5 times in the speed of prediction, which contributes a new idea to the prediction of flow field variables.