Optical systems like telescopes are constantly affected by atmospheric turbulence and internal aberration disturbance. Conventional adaptive optics systems (AOS) are proved to be an effective way to eliminate external aberrations caused by atmospheric turbulence, however, when internal aberrations with high amplitude emerge, the problem becomes complicated. The double overlap AOS structure presented exploits an independent inner channel AOS to correct internal aberration disturbance, and an outer channel AOS mainly external to atmospheric turbulence. Furthermore, the correction abilities of this structure and conventional AOS are analyzed and compared. In addition, their correction performances under the situation where two aforementioned type aberrations simultaneously exist are numerically simulated. Results show that reasonably designed operating conditions of double overlap AOS make the performance better than conventional AOS, especially when internal aberrations become relatively stronger.