The linear and nonlinear gap resonances in a free-rolling moonpool are investigated using a two-dimensional in-house code based on the constrained interpolation profile method. This study primarily focuses on the effects of roll motion on hydrodynamic characteristics, taking into account both the linear gap resonance and the nonlinear process-driven gap resonances. The analysis of the incident-wave height is conducted to illustrate the relationship between higher-order harmonics and nonlinear gap resonances. Numerical results demonstrate that the resonant frequency is insensitive to the roll motion. However, the roll response plays an important role in influencing the vertical wave loads on the barges and affecting the energy conversion pattern in the fluid field. According to the analysis of the incident-wave height parameter, the magnitudes of resonance at the linear and nonlinear resonant points are approximately in sub-linear and superlinear relationships with the incident-wave height, respectively. Moreover, the vortex shedding modes around the entrance of the free-rolling moonpool gradually transit from being dominated by the pairs of vortices to being dominated by the single vortex as the gap resonance changes from linear to quartic.