Generalized composite aperiodic zone plates (GCAZPs) are proposed to generate clearer images at focal planes. The images can be produced by a target object at infinity based on a collimator. The proposed zone plate consists of the proposed radial zone plate (RZP), whose original radius is not zero, and the common aperiodic zone plate, which has the coincident first-order diffraction area and the same axial first-order diffraction intensity distribution. The GCAZPs are applicable for the other aperiodic zone plates. Moreover, the modulation transfer function curve of the GCAZP is basically above that of the corresponding common aperiodic zone plate. Compared with the common aperiodic zone plates, the GCAZPs have the foci with higher intensity and the images with higher contrast at the same focal planes. In addition, a GCAZP with an arbitrary size can be designed. The construction method of the GCAZP is illustrated in details. Furthermore, it has been also proved numerically and experimentally that the GCAZPs are used to generate the clearer images than the corresponding common aperiodic zone plates. The proposed zone plates are applicable to generate clear images and trap particles stably at multiple planes simultaneously. © 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement