To address the overlapping and defocusing of images with blurred diffuse speckles, a synthetic-aperture occlusion removal algorithm using a microlens array (MLA) is proposed. In this study, a single light-field imaging system with an MLA is designed to acquire data of the original image. The synthetic aperture method is utilized to digitally focus for recognizing occlusion objects in a scene. According to the gray variance value, the threshold value is set to distinguish an occlusion object from the target object. Then, the occlusion object is removed when it is recognized, and the target object can be extracted by refocusing. The experiment shows that the no-reference image quality assessment value is improved by at least 18.83% compared with that using other similar algorithms. The proposed method not only improves the image quality, but also presents 3D information of the scene. It also obtains the target image with a high contrast and high signal-to-noise ratio.