In this study, a high-resolution and high-accuracy 2D pseudo-spectral numerical model (Diamessis et al. 2005) [23] is applied to investigate the boundary layer flows under a surface solitary wave. The numerical results are compared with the analytical solution derived by Liu & Orfilla (2004)[24], and the experimental data obtained from a series of U-tube experiments provided by Sumer et al. (2010)[21]. Define the Reynolds number as Re = aU0m /[nu], where U0m is the maximum free-stream velocity, 2a the corresponding fluid particle displacement, and [nu] the fluid viscosity, Sumer et al. (2010)[21] tested the boundary layer flow under the soliton-like pressure gradient for Re ranging from 2.8 x 104 to 2.0 x 106 . They reported that as the Reynolds number increases, the boundary flow experiences from laminar regime to the transitional flow regime where a regular array of 2D vortex tubes was generated in the boundary layer; and then to the turbulent flow regime where the 3D turbulent spots appear. In this study, we design three cases following the Sumer et al. (2010)'s[21] experimental setup in the transitional flow regime (Re ranging from 2.0 x 105 to 6.0 x 105 ) to examine the characteriscs and the evolution of the vortex coherent structures in the wave boundary layer. An universal graph of the evolution of the normalized bed shear stress without generalization of the vortex tubes within different Reynolds number is shown as a preliminary discuss of the near-bed flow behaviour. The vortex coherent structures are then triggered by inserting numerical noises, we conclude that during the deceleration stage, flow reversal occurs near the boundary layer, the Kevin-Helmholz (K-H) instability is found to be the main mechanism responsible for the generation of the 2D vortex tubes. The evolution of the shear layer instability is examined and discussed. The evolution of the shear layer instability is also provided in this study by examing the development of the vortex structures and the spatio-temporal description of the bottom shear stress. The changes of the vorticity field are quantified by vortex tube characteristics, such as the magnitude, size and trajectory. To investigate the effect of tsunami-typed surface wave on the coherent structure in boundary layer, a further study applying the non-symmetric surface solitary wave is also provided.