An efficient algorithm is developed for solving a special reverse convex programming problem: \(\min\{cx\mid x\in D,\;f(x)\leq 1\}\), where \(c\in \mathbb{R}^ n\), \(D\) is a polytope and \(f\) is a quasiconcave function on \(D\) possessing the following rank two property: There exist two linearly independent vectors \(c^ 1, c^ 2\in \mathbb{R}^ n\) such that for all \(x\in D: z\in \mathbb{R}^ n\), \(c^ i z\geq 0\) \((i=1,2)\Rightarrow f(x+ z)\geq f(x)\). Computational results are presented and discussed.