Based on the anisotropic crystallographic theory, a model of low cycle fatigue (LCF) life time of a nickel base single crystal in a multiaxial stress state is proposed. The model indicates that LCF life time has a power relationship to total shear strain of modified octahedral slip. The detail distributions of stress and strain in a hellow cylinder specimen under tension torsion LCF loadings are analyzed in detail. The LCF life time model has been confirmed successfully using the results of tension torsion LCF tests of CMSX 2 NI base single crystal superalloy.