The special two-phase micro-structure of nickel-based single crystal superalloy makes it anisotropic. Creep tests of three different orientations of the single crystal superalloy DD6 were carried out under 980℃, indicated that the creep failure of superalloy is the initiation of micropores and the propagation of microcracks, which is caused by dislocation motion. Transmission electron microscopy (TEM) was used to observe the dislocation morphology of monocrystals in [001], [111] and [011] orientation at the initial stage of creep, found matching the characteristics of the octahedral sliding system activated, the hexahedral sliding system activated and the simultaneous motion of the two sliding systems respectively. Based on the crystal plasticity theory, the creep constitutive model and creep damage model?under variational stress conditions were established with Orowan effect and dislocation blocking effect considered, meanwhile, the model parameters were fitted according to the creep curve obtained from the test. Moreover, the finite element simulation results of the model and creep fracture morphology of monocrystalline materials mutually confirm and explain the anisotropic behavior of monocrystalline creep.