This paper focuses on the enhancement or suppression effect of flow-induced vibration (FIV) caused by symmetrically installed groove structures with different shapes under high Reynolds numbers. The fluid flow field is simulated using the non-constant two-dimensional Reynolds-averaged Navier-Stokes (2D-RANS) equation and the SST k-ω turbulence model. A cylinder attached to four different groove shapes (square, triangular, semicircular, and two quarter-circle splices) is simulated for each shape of the groove with five mounting angles. The oscillatory amplitude, frequency response, displacement time history curve, vortex shedding mode, and energy harvesting characteristics are analyzed for each working condition at 2 < U* < 14 and 2.02 × 104 <Re < 1.44 × 105. The results show that the cylinder with different groove shapes and installation angles have different dynamic responses. The oscillatory amplitude of the square groove bluff body with α = 30°, 60°, and 150° is basically enhanced compared to the smooth cylinder, and the working bandwidth is increased as well. For the square groove placed at α = 60°, the oscillatory amplitude increases by 100% compared to the smooth cylinder, and the working bandwidth of the square groove at α = 90° is reduced by 50%. For the square groove body with α = 120°, the amplitude is enhanced, but the working bandwidth is reduced. The working bandwidth of the triangular groove is widened at all five angles, with the α = 60° groove being optimal, widening by 75%. Except for the triangular groove with α = 90°, the amplitude is improved to some extent compared with the smooth cylinder. The working bandwidths of the semicircular grooves are widened, and the improvement effect of α = 150° is the smallest of the five angles. For the two quarter-circle splices grooves, the grooves arranged at α = 30°, 90°, 120°, and 150° have a decrease in amplitude when U* = 6, and more pronounced at 90° and 120°. Two quarter-circle spliced groove cylinders with α = 120° have the best amplitude enhancement effect.