Abstract: At present, although the theory analysis of GA’s convergence focuses attention on limit behavior, it is lacking global dynamic researching In this paper, the GA’s global dynamic shape is first analyzed in accordance with a simple 2 bit problem The common evolution operators and their combination are described formally Four mathematic models are established based on different parameters selection of canonical genetic algorithms The effects are discovered that every operator has on GA’s dynamic shape through the attraction analysis of model’s fixed points The global convergence is proved for this problem There are two attractive fixed points, one saddle point （or one ejective point） and no other fixed point or period point in the mathematic models when two competitive local peaks exist Which local peak can be converged is determined by the position of initial condition in status space, and the proportion of each domain is determined by the model’s parameters