Reversed-shear Alfvén eigenmodes were observed for the first time in a helical plasma having negative q₀'' (the curvature of the safety factor q at the zero shear layer). The frequency is swept downward and upward sequentially via the time variation in the maximum of q. The eigenmodes calculated by ideal MHD theory are consistent with the experimental data. The frequency sweeping is mainly determined by the effects of energetic ions and the bulk pressure gradient. Coupling of reversed-shear Alfvén eigenmodes with energetic ion driven geodesic acoustic modes generates a multitude of frequency-sweeping modes.