Arachidonic acid (AA), a representative omega 6-polyunsaturated fatty acid (PUFA), is a precursor of 2-series prostaglandins (PGs) that play important roles in inflammation, pain, fever, and related disorders including cardiovascular diseases. Eating fish or supplementation with the omega 3-PUFAs such as eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) is widely assumed to be beneficial in preventing cardiovascular diseases. A proposed mechanism for a cardio-protective role of omega 3-PUFAs assumes competition between AA and omega 3-PUFAs for cyclooxygenases (COX), leading to reduced production of 2 series PGs. In this study, we have used a systems biology approach to integrate existing knowledge and novel high-throughput data that facilitates a quantitative understanding of the molecular mechanism of omega 3- and omega 6-PUFA metabolism in mammalian cells. We have developed a quantitative computational model of the competitive metabolism of AA and EPA via the COX pathway through a two-step matrix-based approach to estimate the rate constants. This model was developed by using lipidomic data sets that were experimentally obtained from EPA-supplemented ATP-stimulated RAW264.7 macrophages. The resulting model fits the experimental data well for all metabolites and demonstrates that the integrated metabolic and signaling networks and the experimental data are consistent with one another. The robustness of the model was validated through parametric sensitivity and uncertainty analysis. We also validated the model by predicting the results from other independent experiments involving AA and DHA-supplemented ATP-stimulated RAW264.7 cells using the parameters estimated with EPA. Furthermore, we showed that the higher affinity of EPA binding to COX compared with AA was able to inhibit AA metabolism effectively. Thus, our model captures the essential features of competitive metabolism of omega 3- and omega 6-PUFAs.