In this article, we consider the second-grade fluid equations in 2D exterior domain Ω with homogeneous Dirichlet boundary conditions. For initial data u 0 ∈ H 3 (Ω) , the second-grade fluid equations is shown to be globally well-posed. Furthermore, for arbitrary T > 0 and s ≥ 3 , we prove that the solution belongs to L ∞ ([ 0 , T ] ; H s (Ω)) provided that u 0 is in H s (Ω) .