Wake generated by wind turbine can greatly influence the performance of downstream turbine. To better understand the wake Self-similarity characteristics of vertical axis wind turbine (VAWT), the shear stress transport (SST) turbulence model with the addition of the γ-Reθ transition model is performed to model a two-blade VAWT at different operating conditions. The simulated blade surface pressure and torque are compared with existing experimental results for validation. Results show that, the simulated results after considering the transition model are more consistent with the experimental results. Analysis of the flow field shows that the average streamwise velocity of the wake in the horizontal plane under different tip speed ratios is asymmetry, but symmetric in the vertical plane. Further analysis indicates that, at different downstream positions, the non-dimensional streamwise velocity deficit in the vertical plane remains Self-similarity and basically coincides with the Gaussian distribution curve exclude the wake edges. In addition, the larger the tip speed ratio, the easier streamwise velocity deficit reach Self-similarity state at downstream of the VAWT. The results of this study will be helpful to establish the wake model of the VAWT.