Abstract: Based on the classical GM(1,1) model of integer (fractional) accumulation, we propose the grey model of complex accumulation (which is denoted by CAGM z(1,1) for some complex number z ∈ C ). This formulation extends the choice of Grey model's parameter from the real axis to the complex plane. We claim that all complex accumulated generating operators admit a1 dimensional additive complex Lie group's structure, which is isomorphic to C. This construction brings Lie group's theory in Grey model theory for the first time, and lays a foundation for introducing Lie group's tools in the grey system. The method of nilpotent matrix E1 of index n and Taylor series could avoid any usage of existing popular Γ functions, which also provides an efficient way for computer programming. As a novel method, accumulated generating operators of complex order could adjust weights between old information and new information, between the real part and the imaginary part simultaneously, better simulation and prediction results could be expected. The advantages of CAGM z(1,1) model are discussed with several cases, better simulation and prediction results are presented.