In this work, to study the effects of stress triaxiality, temperature, and strain rate on the fracture behaviors of a single-crystal Nickel-base superalloy, a series of experiments over a temperature range of 293 to 1373 K, strain rate range of 0.001 to 4000/s, and stress triaxiality range of −0.6 to 1.1 are conducted. Anomalous peak of stress is noticed in the yield stress versus temperature curves, and strain rate effect on the anomalous peak of yield stress is analyzed. The anomalous peak shifts to higher temperature as the strain rate increases. Then the effects of stress triaxiality, temperature, and strain rate on its fracture behaviors, including strain to fracture, path of crack propagation, and fracture surface, are observed and analyzed. A valley of the fracture strain is formed in the fracture strain versus temperature curve over the selected temperature range. The micrograph of fracture surface is largely dependent on the temperature, stress triaxiality, and strain rate. Finally, the original Johnson-Cook (J-C) fracture criterion cannot describe the effect of stress triaxiality and temperature on the fracture behaviors of single-crystal Nickel-base superalloy. A modified J-C fracture criterion is developed, which takes the anomalous stress triaxiality and temperature effects on the fracture behaviors of single-crystal Nickel-base superalloy into account.