Recent studies have demonstrated the superior efficacy of bilateral internal thoracic artery (BITA) grafts compared to other graft methods in treating coronary artery disease. Competitive flow (CF) is a primary factor contributing to graft failure in the long term. For the first time, the CF of the BITA-Y graft has undergone rigorous numerical analysis. Through the application of transit time flow measurement (TTFM) and hemodynamic parameters, this study provides a new perspective on graft performance. Simulation results indicate that average flow, TTFM, and hemodynamic parameters fall within the critical range for stenosis severities below 90%. Specifically, at 80% stenosis, the mean graft flow (MGF) and pulsatility index (PI) of the left internal thoracic artery (LITA) were 0.071 cc/s and 27, respectively, while those of the right internal thoracic artery (RITA) were 0.211 cc/s and 11. With increasing stenosis severity, TTFM parameters remained within the clinical permissible limit (MGF > 0.34 cc/s and PI < 5). At 95% stenosis severity, the MGF and PI for LITA were 0.526 cc/s and 1.2, respectively, while those for RITA were 0.790 cc/s and 0.9. The results indicate the presence of competitive flow within the BITA-Y graft for stenosis severities below 90% area reduction, suggesting a potential risk of graft failure in the long term. Additionally, the results indicated that when there are significant differences in stenosis severity between the two native arteries, the BITA-Y graft is not optimal due to CF, characterized by low MGF and high reverse flow.