Abstract: The general Julia sets (the general J sets for short) are generated from the iterated functions system f_\omega, c=z^\omega+c(\omega \in \mathrmC, c \in \mathrmC). Based on the escape time algorithm, by changing the parameters \omega, c in f_\omega, c(z)=z^\omega+c(\omega \in \mathrmC, c \in \mathrmC), the corresponding fractal images of general J sets were produced with the platform of \mathrmVC++. In comparison with output graphs, an important conclusion of the symmetry of general J sets by only changing parameter c is draw n and proved theoretically. Similarly, through the analy ^- sis to graphs of general J sets by the change of both \omega and c, a corresponding conclusion is also given.