An effective strategy comprising two phases is proposed to determine the thermodynamically dominant pathways in a metabolic network of a given phenotype, involving several metabolic reactions. In the first phase, stoichiometrically feasible metabolic pathways are exhaustively identified through the flux balance analysis and the graph-theoretic method based on P-graphs. In the second phase, thermodynamically dominant pathways are selected from these stoichiometrically feasible metabolic pathways on the basis of the Gibbs free energy change of reaction. The proposed strategy's efficacy is demonstrated by applying it to two E. coil models: one is for maximal acetate and ethanol production, and the other is for maximal poly(3-hydroxybutyrate) production.