In　this　article,　we　propose　and　analyze　an　energy　stable,　linear,　second-order　in　time,　exponential　time　differencing　multi-step　(ETD-MS)　method　for　solving　the　Swift–Hohenberg　equation　with　quadratic–cubic　nonlinear　term.　The　ETD-based　explicit　multi-step　approximations　and　Fourier　collocation　spectral　method　are　applied　in　time　integration　and　spatial　discretization　of　the　corresponding　equation,　respectively.　In　particular,　a　second-order　artificial　stabilizing　term,　in　the　form　of　Aτ2∂(Δ2+1)u∂t,　is　added　to　ensure　the　energy　stability.　The　long-time　unconditional　energy　stability　of　the　algorithm　is　established　rigorously.　In　addition,　error　estimates　in　ℓ∞(0,T;ℓ2)-norm　are　derived,　with　a　careful　estimate　of　the　aliasing　error.　Numerical　examples　are　carried　out　to　verify　the　theoretical　results.　The　long-time　simulation　demonstrates　the　stability　and　the　efficiency　of　the　numerical　method.　©　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature　2024.