With its wide use in different fields, the problem of the convergence of simple genetic algorithms (GAs) has been concerned. In the past, the research on the convergence of GAs was based on Holland s model theorem. The diversity of the evolutionary population and the convergence of GAs are studied by using the concept of negentropy based on the discussion of the characteristic of GA. Some test functions are used to test the convergence of GAs, and good results have been obtained. It is shown that the global optimization may be obtained by selecting appropriate parameters of simple GAs if the evolution time is enough.