Single crystal nickel base superalloys, such as Chinese material DD6 have been used in gas turbine blade in China more and more widely. In order to make better use of single crystal superalloys with many excellencies, constitutive models have been developed. In this paper, general method of crystallographic constitutive modeling was summarizes and a new constitutive model, based on crystallographic theory was proposed with phenomenological models' advantages. Based on crystallographic slip system principle, the basic slip-based viscoplasticity theory equations were set up on 12 octahedral slip systems and 6 cubic slip systems, total 18 slip systems. In micro-level slip system, the general unified constitutive formulations were used as the flow equations and hardening law. In the model, scalar forms were applied for constitutive equations on slip systems and the number and types of active slip systems were used to describe the material anisotropy, which was satisfied automatically by slip systems not anisotropic tensors and. The experimental and calculation results of two kind single crystal superalloys PWA1480 and DD6 were compared. The model had the capability to predict many mechanical response and analyze structure of single crystal superalloys. The modeling procedures and results showed that this crystallographic model had more clear physical meaning and was exact.