Volumetric images have a three-dimensional (3D) view, in which viewers can examine their characteristics from any angle. The more accurate the digital representation of volumetric images, the more precise and valuable the assessment of what these images represent. The representation of volumetric images is a significant area of study in pattern recognition and computer vision. Recently, volumetric image analysis using orthogonal moments with fractional order has opened up a new study pathway, which has led scholars to discover many real-life applications through investigating efficient algorithms to represent the features of 3D images. In this study, a new set of 3D shifted fractional-order Gegenbauer moments (FrGMs) for volumetric image representation is proposed. First, a mathematical description of the shifted Gegenbauer moments for 3D images is presented. Second, a fast, highly accurate method for calculating the fractional-order shifted Gegenbauer moments of 3D images is introduced. Finally, the efficiency of the proposed FrGMs is evaluated through various suitable experiments and compared with existing methods in terms of the reconstruction of 3D images, the invariability property, sensitivity to noise, and computation time. The experimental results clearly show that FrGMs outperform existing related algorithms