Abstract: We introduce a concept of a semi-uniform attractor for an evolution process. A theorem for existence result of semi-uniform attractor are given in this paper. Although the invariance is not involved, but it can induce a semi-uniformly compact pullback attractor. Moreover, under some suitable assumptions, we show that the non-autonomous Kuramoto-Sivashinsky equation has a semi-uniform attractor and a semi-uniformly compact pullback attractor.