We study forward self-similar solutions to the 3-D Navier-Stokes equations with the fractional diffusion (−Δ)^α. First, we construct a global-time forward self-similar solutions to the fractional Navier-Stokes equations with 5/6 <α ≤1for arbitrarily large self-similar initial data by making use of the so called blow-up argument. Moreover, we prove that this so-lution is smooth in R^3×(0, +∞). In particular, when α =1, we prove that the solution constructed by Korobkov and Tsai (2016) [16]satisfies the decay estimate by establishing regu-larity of solution for the corresponding elliptic system, which implies this solution has the same properties as a solution which was constructed in Jia and Šverák (2014) [13].