The Omega ratio is a recent performance measure. It captures both the downside and upside potentials of the constructed portfolio, while remaining consistent with utility maximization. In this paper, a new approach to compute the maximum Omega ratio as a linear program is derived. While the Omega ratio is considered to be a nonconvex function, the authors show an exact formulation in terms of a convex optimization problem and transform it as a linear program. The convex reformulation for the Omega ratio maximization is a direct analog of the mean-variance framework and the Sharpe ratio maximization.