In this paper, a method to predict ductile fracture under low cyclic loading condition is proposed. Then it is compared with test results of surface cracked pipes which is conducted by Battelle Institute. A&F nonlinear kinematic hardening model is adopted to describe material behavior under cyclic loading condition and energy-based damage model is applied to simulate ductile crack growth. The energy-based damaged model is depending on multi-axial fracture strain energy. To apply this model, two parameters should be determined from tensile and C(T) test results under monotonic loading condition. One is multi-axial fracture strain energy Wf and the other is critical damage value °c . From the determined damaged model, it is enable to simulate surface cracked pipe tests under low cyclic loading condition.