Vortex-induced vibrations are a type of flow-induced vibrations caused by alternating lift forces. With increasing demand for renewable energy, the application of vortex-induced vibrations to renewable energy has been widely studied. Vortex-induced vibrations for aquatic clean energy (VIVACE) converter is a renewable energy device that generates electricity from rivers or oceans using vortex-induced vibrations. To increase the design life and power harnessing capacity of the VIVACE converter, the estimation of fluid forces due to vortex-induced vibrations is essential. Herein, vortex-induced vibrations were experimentally tested, and their amplitude and frequency response were measured. The amplitude results showed four different branches: initial branch, upper branch, lower branch, and desynchronization range. According to the fluid force coefficient results, the maximum lift coefficient occurred at the upper branch. Additionally, a mathematical model is proposed to estimate fluid forces due to vortex-induced vibrations without using measurement devices. This mathematical model enables the estimation of fluid force coefficients and phase lag using amplitude and frequency response of vortex-induced vibrations.