In this paper, we are concerned with a high-order energy-dissipation-preserving scheme for the time-fractional Swift-Hohenberg equation. To this end, we apply the variable-step L \(2\text{- }1_\sigma \) formula and discrete gradient method to approximate the fractional derivative and nonlinear potential function, respectively. In virtue of the discrete gradient structure of the L \(2\text{- }1_\sigma \) formula proposed in a recent work (Liao et al., J. Sci. Comput., 99 (2024), 46), we study a discrete variational energy and prove that it is asymptotically compatible and dissipative. Furthermore, an enhanced discrete fractional Gronwall inequality is introduced to establish the convergence in \(L^2\) norm. Extensive numerical experiments validate the theoretical result and illustrate the efficiency and accuracy of the proposed scheme in long-time simulation.
