Let \(S^{n+p}_p(c)\) be a de Sitter \((n+p)\)-space of constant curvature \(c>0\), and \(M\) be an \(n\)-dimensional complete space-like submanifold in \(S^{n+p}_p\). The main result of this paper is as follows. Assume that \(M\) has flat normal connection, parallel mean curvature vector field and constant scalar curvature. Then \(M\) is total umbilical if either (i) the sectional curvature of \(M\) is negative; or (ii) the length square of the second fundamental form \(\sigma \) of \(M\) satisfies \(\|\sigma \|^2<\frac{n^2H^2}{n-1}-2c\). The reviewer thinks that the assumption conditions in theorems of this paper may be too strong.