This work focuses on molecular creep behavior of carbon fiber/epoxy interface under sustained loads at different levels. Threshold stress and energy barrier for the onset of interfacial creep failure under peeling loads are found greater than those under shearing. Microstructural changes during creep show that the epoxy has a large and irreversible deformation under peeling loads, denoted as a yielding process in the peeling case. The yielding process in the peeling case dissipates the applied energy in the epoxy structure. Therefore, the interface shows a stronger resistance to the peeling and the shearing is more critical during composite failure.