In this paper, the lensing functions and imaging abilities of a quasi-periodic nanohole array in a metal screen have been theoretically investigated and demonstrated. Such an optical binary mask with nanoholes designed in an aperiodic arrangement can function as an ultra-thin planar optical lens, imaging complex structures composed of multiple light sources at tens of wavelengths away from the lens surface. Via resolving two adjacent testing objects at different separations, the effective numerical aperture (N.A.) and the effective imaging area of the planar optical lens can be evaluated, mimicking the imaging function of a conventional lens with high N.A. Furthermore, by using the quasi-periodic nanohole array as an ultra-thin planar optical lens, important applications such as X-ray imaging and nano-optical circuits may be found in circumstances where conventional optical lenses cannot readily be applied.