In this paper, we investigate the existence of infinitely many solutions for the following fractional Hamiltonian systems: [equation presented] where α ∈ (1/2, 1), t ∈ u ∈ ⁿ, L ∈ C(ⁿ²) is a symmetric and positive definite matrix for all t ∈ W ∈ C¹(× ⁿ), and δW is the gradient of W at u. The novelty of this paper is that, assuming there exists l ∈ C such that (L(t)u, u) = l(t)|u|² for all t ∈ u ∈ ⁿ and the following conditions on l: inft∈ l(t) 0 and there exists r00 such that, for any M 0 m({t ∈ (y-r<inf>0</inf>, y + r<inf>0</inf>)/l(t)≤ M}) → 0 as |y| → ∞ are satisfied and W is of subquadratic growth as |u| → +∞, we show that (0.1) possesses infinitely many solutions via the genus properties in the critical theory. Recent results in Z. Zhang and R. Yuan [24] are significantly improved.