The phenomenon of vibration interference among multiple risers is one of the hot topics in ocean engineering. As a basic model of multi-pipe systems, the dual staggered flexible pipe system is widely used to analyze vortex-induced vibration (VIV) behavior. In this paper, the VIV characteristics associated with a dual staggered flexible pipe system is investigated by a two-way fluid-structure interaction method. The results show that the influence of staggered angles on the in-line and cross-flow vibration responses of upstream and downstream pipes is distinctly different. Owing to the short-range interference between dual pipes, the amplitude of downstream pipe is generally larger than that of upstream pipe, more likely to demonstrate "multi-mode competition" phenomenon. Due to the effect of staggered arrangement and small spacing ratio, the interation between fluid and dual pipes is relatively strong, leading to the failure of forming regular shedding vortex in the wake of the dual pipe system. Through the analysis of vibration response and phase difference at the peaks and valleys of RMS amplitude envelopes, related to the dual staggered flexible-pipe, it is found that when the staggered angle of dual flexible-pipes increases from 15° to 60°, the votex shedding mode changes from "2P" to "2S", the fluid excitation frequency and intensity of the upstream pipe become weakened, and the vibration displacement phase difference and lift force coefficient phase difference of the upstream and downstream pipes are reduced.