To address the significant challenges in predicting high-dimensional chaotic systems, this paper introduces a novel hybrid strategy that combines proper orthogonal decomposition (POD), which serves as reduced order modeling (ROM), with next generation reservoir computing (NGRC), a data-driven prediction model. The POD-NGRC strategy harnesses the strengths of POD in extracting principal evolutionary features and reducing system complexity, along with the high accuracy, ease of design, enhanced robustness, and high computational efficiency offered by NGRC. The proposed strategy was employed for predicting chaotic flow-induced vibration (FIV) systems of tube bundles, and the results showed that the hybrid approach demonstrated excellent long-term predictability for a weakly chaotic system and still yielded good short-term prediction for a highly chaotic system. Reducing the FIV of a continuous beam into a 3-degree-of-freedom system using POD modes and training the three time coefficients via a NGRC network with three layers, the hybrid approach can predict time series of a weakly chaotic system with root mean square prediction error less than 1% to 19.3 Lyapunov time, while a three Lyapunov time prediction is still achieved for a highly chaotic system.