Physically based deformation simulation has been studied for many years in computer graphics. In order to simulate more complex materials and better meet the designer's requirements, the anisotropic approach was proposed in recent years. However, most of the existing approaches focus on orthotropic materials. In this paper, a general non-orthogonal constitutive model is presented to simulate the anisotropic deformation behavior for 3D soft objects. The model exhibits different deformation behaviors in different directions by constructing a non-orthogonal coordinate system with covariant and contravariant basis vectors. The constitutive relation between stress and strain is first defined in the non-orthogonal coordinate system, and then transformed into the standard Cartesian coordinate system to represent the global non-orthotropic materials. In addition, a time-varying method is introduced to track changes of the local coordinate system for each discrete element during deformation, which makes the simulation of non-orthotropic materials more stable. Finally, in order to present desirable features for objects with complex structure, the deformable objects are partitioned into several regions according to their skeletons with the combination of frame-field concept. A corotational linear Finite Element Method(CLFEM) is utilized to complete the simulation. Experiments are presented to demonstrate the efficiency of the non-orthogonal constitutive model.