We design three types of groove structures which are arranged in closely-packedarry (space free), periodic and quasiperiodic orders. The drag reduction properties of these structures are studied by numerical simulations and experimental shear stress measurements. Particularly, the effect of groove arrangement on the drag reduction is elucidated. Based on both the numerical and experimental results, it is found that the quasiperiodic arrangement can obtain more effective drag reduction than the close-packed groove structure and periodic structure. The underlying mechanism of the drag reduction is analyzed by vortex redistribution caused by the groove structures. The high-speed flow can be modulated by the disturbance wave resulting from the quasi-periodic groove structure, forming stripe-like flow patterns arranged in quasiperiodic style. This restrains the formation of big vortex in both the spanwise and the streamwise directions, hence leading to substantial drag reduction. Furthermore, the modulation effect on the streamwise vortex is more remarkable than on spanwise vortex, suggesting that the modulation of streamwise vortex plays a more important role in the drag reduction.