In this work, bases on the reproducing kernel theory and collocation method, we study the space Riesz fractional Navier-Stokes equations, and propose the numerical method to solve it. Firstly the new base space can be constructed by the spline and reproducing kernel space. The ε-approximate solution in binary spline space in the form of finite terms can be derived. Through using the collocation method, the approximate problem is solved. In addition, we provide analysis of the stability and convergence. In final, two numerical examples are provided to show the effectiveness of our method.