Flutter seriously affects the safety and reliability of aeroengine. In this paper, influence coefficient method (ICM) and traveling wave method (TWM) are used to calculate the aerodynamic damping of transonic fan blades of civil aviation engine at different nodal diameters (NDs) and structural modes. The results of two methods are basically consistent but the ICM only needs to simulate seven passages for all of the NDs, which has higher computation efficiency. The results show that under the design condition, the first three structural modes of the blade are aero-elastic stable for each ND, and the aerodynamic damping gets the minimum at ND1 for the first bending mode. As the back pressure deviates from design condition towards choking or stall, the aerodynamic damping obviously decrease and even negative aerodynamic damping occurs at normalized mass flow rate of 0.950. Dynamic mode decomposition (DMD) is applied to analyze the transient pressure on vibrating blade surface. Dominant flow structures like shock wave oscillating and corresponding frequency on blade surface can be acquired through DMD method. TWM simulation with DMD analysis indicates that the shock wave changes the phase of the pressure in the region next to downstream of the shock wave, which makes the aerodynamic work concentrate locally.