Flexible cylindrical structures, such as top-tensioned risers (TTRs) and tethers of tension leg platforms (TLPs), usually vibrate under the combined excitation of vortex shedding and time-varying axial tension. Helical strakes are widely used to suppress vortex-induced vibration (VIV). The VIV suppression effectiveness of helical strakes for a flexible cylinder under axial tension excitation is still unknown. Model tests were conducted to investigate the effect of time-varying axial tension on VIV suppression for a flexible cylinder fitted with helical strakes. Three tension amplitude ratios (Tv/Tc = 0.1, 0.2 and 0.3, where Tv is the amplitude of the varying tension and Tc is the constant axial tension) and four tension frequency ratios (fv/f1 = 0.5, 1.0, 2.0 and 4.0, where fv is the frequency of the varying tension and f1 is the fundamental natural structural frequency) were considered. The vibration displacements were reconstructed using the measured strains by the modal analysis method. The dominant mode, response frequency and displacement amplitude were determined to show the influence of axial excitation on the dynamic characteristics of the flexible cylinder attached with helical strakes. When the reduced velocity is low, the second-order mode vibrations of the straked cylinder with axial excitation are excited. Due to the axial excitation, the straked cylinder has large cross-flow (CF) and in-line (IL) displacements at low reduced velocities. The displacement contours in the case of fv/f1 = 1.0 are remarkably different from those in other cases. When the reduced velocity increases, the effect of vortex shedding is enhanced. Both fv induced by axial excitation and the fn induced by vortex shedding are prominent, meaning that both vortex shedding and axial excitation affect the vibration of the straked cylinder. Under axial excitation, the IL displacements of the straked cylinder are enlarged, especially in the case of fv/f1 = 1.0. Axial excitation can reduce the VIV suppression efficiency of helical strakes.