The paper is concerned with the non-autonomous modified Swift-Hohenberg equation u(t) + Delta(2)u + 2 Delta u + au + b vertical bar del u vertical bar(2) + u(3) = g(x,t). It is shown that a uniform attractor exists in H-0(2) when the external force only satisfies the translation bounded condition instead of translation compactness. In order to overcome the difficulty caused by the critical nonlinearity terms u3 and the parameter b belonging to the real set R, we take advantage of the Gagliardo-Nirenberg inequality several times.