A numerical study of vortex-induced vibration (VIV) related to a flexible pipe system subjected to external current and internal flow was performed mainly to investigate the complex vibration response of the flexible pipe due to the coupled effect of external current and varying-density internal flow. The numerical model was validated through mesh dependency and fluid-structure interaction (FSI) analysis. A coupled correlation analysis method, combined with a 3D position-frequency-energy (PFE) spectral analysis technique, was proposed to reveal the spatial multi-mode competition along the flexible pipe span. It is shown that the increase in the velocity and density of internal flow amplifies the spanwise in-line mean deflection, but has limited effect on the dominant vibration mode. The vibration modes at the amplitude peak and trough are significantly different. High order vibration modes, characterized by classical“8”-shaped vibration trajectories, are dominant around the amplitude peak, but low order vibration modes become predominant, and phenomena of spatial multi-mode competition with chaotic vibration trajectories are favorable at the amplitude trough.