(Kim, et al., 2016;Baarholm, et al., 2006;Trim, et al., 2005)Oil and gas production riser systems need to be designed considering a wide band quarter-modal analysis which contains low-, wave-, VIV(Vortex induced vibration) frequencies. The VIV can be separated into cross-flow(CF) and in-line(IL) components. In this study, the various idealized tri-and quarter-modal spectra are suggested to analyze fatigue damage on the production riser system. In order to evaluate the fatigue damage increment caused by the IL's motion, tri-and quarter-modal spectral fatigue damages are calculated in time domain. And the fatigue damage calculated from two different modal spectra are compared quantitatively. Then the suitability of existent wide band fatigue damage models for quarter modal spectrum was evaluated by comparison of frequency domain calculation and time domain calculation. The result show that although spectral density of IL motion is not remarkable in quantity, the effect on the fatigue damage is significant and existent fatigue damage models are not adequately estimating damage by quarter-modal spectra.