In this paper, the authors transform the problem of undirected graph drawing to the problem of function optimization, then use genetic algorithms to find approximate optimal solutions of the objective function, and thus obtain a general structure of undirected graph drawing algorithms. The characters of the new method are: the structures of the different graph drawing algorithms are the same, the difference exists only in the objective functions which reflect aesthetic criteria. The advantages of the method are: unified algorithms, simplicity, easy modification and parallelism, and it can be used to draw non-connected graphs directly.