Under different parameter conditions, Chua’s oscillator may display two types of coexisted singlescrolled periodic oscillations which are symmetric to each other, or behaves in single doublescrolled periodic oscillation with symmetric structure. With the variation of the periodic excitation, the two coexisted periodic solutions may evolve to two symmetric chaotic attractors respectively. Periodic windows as well as perioddoubling sequence can be observed in the evolution. Furthermore, for relatively low frequency related to the excitation, the two coexisted chaotic attractors may interact with each other to form an enlarged chaotic attractor, and the trajectory may be around the two subattractors in turn for relatively long time. While for the doublescrolled periodic oscillation, the periodic excitation may cause two coexisted quasiperiodic movements, which may interact with each other to form a single quasiperiodic oscillation and finally evolve to a doublescrolled chaotic attractor.