This paper proposes an improved genetic algorithm for producing aesthetically pleasing drawings of general undirected graphs. Previous undirected graph drawing algorithms draw large cycles with no chords as concave polygons. In order to overcome such disadvantage, the genetic algorithm in this paper designs a new mutation operator single-vertex- neighborhood mutation and adds a component aiming at symmetric drawings to the fitness function, and it can draw such type graphs as convex polygons. The improved algorithm is of following advantages: The method is simple and it is easy to be implemented, and the drawings produced by the algorithm are beautiful, and also it is flexible in that the relative weights of the criteria can be altered. The experiment results show that the drawings of graphs produced by our algorithm are more beautiful than those produced by simple genetic algorithms, the original spring algorithm and the algorithm in bibliography [4] .