We design two types of 8-fold quasi-period short groove structures which are arranged in single row and three rows respectively The flow field in the turbulent boundary layer and the total stress over these groove surfaces are numerically simulated by using Reynolds average Navier-Stokes equation and turbulence model. It is shown that the 8-fold quasi-periodic structure has good drag reduction effect compared with the periodic and disorder structures, especially for structure arranged in three rows. The results are also confirmed by the sheer stress measurements which are performed on substrates with the designed structures. By analyzing the distribution of flow field, we find that the quasi-periodic structure effectively inhibits the intensity of vortex, reduces the turbulent dissipation rate, and keeps the stripe phase stable. Furthermore, by using the two-dimensional grating model, it is found that the 8-fold quasi-periodic structure can reduce spectrum intensity in the large angle direction, revealing that the inhibition of the extension of coherence disturbance waves is responsible for the drag reduction effect, which is also confirmed by the flow field analysis.