Although the left internal mammary artery (LIMA) bypass graft is the best choice for surgical revascularization, its hemodynamics are still complex and can result in long-term graft failure. Here, we performed a hemodynamic analysis of the LIMA-coronary artery with end-to-side/side-to-side anastomoses based on 15 patient-specific CTA images at various postoperative periods. We hypothesize that hemodynamic patterns are determined by the interplay of LIMA geometry, anastomotic configuration, and severity of native coronary artery stenosis, which are strongly affected by the postoperative time. A 3D finite volume method with the inlet pressure wave and outlet resistance boundary conditions was used to compute the distribution of pressure and flow, from which the time-averaged wall shear stress (TAWSS), oscillation shear index (OSI), time-averaged WSS gradient (TAWSSG), and transverse WSS (transWSS) were determined. To characterize the hemodynamic environment, we defined surface area ratios of low TAWSS (≤4dynes/cm2), high OSI (≥0.15), TAWSSG (≥500dynes/cm3), and transWSS (≥6dynes/cm2) in the LIMA graft and at the anastomosis between LIMA graft and coronary artery. These ratios were determined by the interplay of multiple morphometric parameters in the LIMA-coronary artery, but increased with postoperative time. These findings have significant implications for understanding LIMA graft patency.