When a modern large-scale wind turbine operates in natural environment, ambient turbulence increases the complexity of vortex-induced vibration (VIV) of the wind turbine airfoil. This is clearly different from the relatively simple response observed in the case of uniform incoming flow. In this study, the effect of turbulent flow on the VIV response of a wind turbine airfoil is investigated with an identified wake oscillator model. Compared with the uniform incoming flow, inflow turbulence drives the airfoil to frequently enter or exit the frequency lock-in region, and thus the vibration response represents intermittency characteristics. Then, nonlinear time series analysis methods including phase space reconstruction, recurrence plots and complex network theory are used to compare the vibration response of the airfoil under different inflow conditions. It is shown that the complex network can directly reflect the phase space topology of time series, and effectively distinguish the intermittency and quasi-periodic characteristics of the vibration response under different inflow conditions. It is a new perspective to study the VIV response of wind turbine airfoils under turbulent flow.