Positron emission tomography (PET) can provide functional images and identify abnormal metabolic regions of the whole-body to effectively detect tumor presence and distribution. The filtered back-projection (FBP) algorithm is one of the most common images reconstruction methods. However, it will generate strike artifacts on the reconstructed image and affect the clinical diagnosis of lesions. Past studies have shown reduction in strike artifacts and improvement in quality of images by two-dimensional morphological structure operators (2D-MSO). The morphological structure method merely processes the noise distribution of 2D space and never considers the noise distribution of 3D space. This study was designed to develop three-dimensional-morphological structure operators (3D MSO) for nuclear medicine imaging and effectively eliminating strike artifacts without reducing image quality. A parallel operation was also used to calculate the minimum background standard deviation of the images for three-dimensional morphological structure operators with the optimal response curve (3D-MSO/ORC). As a result of Jaszczak phantom and rat verification, 3D-MSO/ORC showed better denoising performance and image quality than the 2D-MSO method. Thus, 3D MSO/ORC with a 3 × 3 × 3 mask can reduce noise efficiently and provide stability in FBP images.