In this paper under review, the author proves a Dirichlet problem for space-like hypersurfaces with prescribed scalar curvature in Minkowski space. Let \({\mathbb R}^{n,1}\) be the Minkowski space \(\displaystyle{{\mathbb R}^{n,1} = \bigl({\mathbb R}^{n+1}, \sum_{i=1}^n dx_i^2 - dx_{n+1}^2 \bigr)}\) with the canonical coordinates \((x_1, \dots, x_{n+1})\). Let \(\Omega\) be a smooth bounded domain in \({\mathbb R}^{n}= \{x_{n+1} = 0\}\) and let \(u\) be a smooth function defined on \(\overline{\Omega}\) satisfying \(\displaystyle{\sup_{\overline{\Omega}} | Du| 0\quad(1\leq k\leq m). \] The author proves if \(\Omega\) is a smooth bounded domain in \({\mathbb R}^3\) and strictly convex, and \(H\) a smooth positive function on \(\overline{\Omega}\), then given a spacelike function \(\varphi\) which is strictly convex, the following Dirichlet problem \[ \left\{ \begin{aligned} {\mathcal H}_2[u] &= H \quad \text{in}\quad \Omega\\ u&=\varphi\quad \text{on}\quad \partial \Omega \end{aligned} \right. \] has a unique solution. In case \({\mathbb R}^4\), the author also shows that if \(H\) is constant, then the Dirichlet problem is also uniquely solvable. The proof relies on a standard continuity method which reduces it to a priori \(C^1\)- and \(C^2\)-estimates. These estimates imply \({\mathcal H}_m\) is uniformly elliptic. The author shows two types of \(C^2\)-estimates, i.e., normal second derivatives estimates and mixed (tangential-normal) second derivatives estimates on the boundary. And the maximum principle is also needed to complete the proof of the main result. The dimension restriction, \(n=3\) or \(n=4\) and \(m=2\), follows from the maximum principle and normal second derivatives estimates, whereas the \(C^1\) global estimate and the tangential-normal second derivatives estimate on the boundary can be obtained without any dimension restriction. The author also conjectures that such a Dirichlet problem might be always solvable in any dimension \(n\) and any \(m\) if \(\Omega\) is a smooth convex bounded domain which has at least \(m-1\) positive principal curvatures at every boundary point.