This paper employs computer algebra techniques to solve the inverse kinematics problem of the 3D Romin Robot. Similar to the approach applied to simple planar robots which is without analyzing the parameter space and is free of any details, we extend it to the 3D Romin Robot by encompassing all conceivable parameters related to the angles and arm lengths of this robot. In particular, we apply the GES-GVW-CGS algorithm (an efficient algorithm for computing the Grobner systems) to partition the parameter space into a finite set of parametric cells and assign a set of parametric polynomials to each cell. We solve the inverse kinematics problem according to each cell containing specific parameter information. All algorithms discussed in this paper are implemented in Maple software. Compared to traditional methods, the proposed approach significantly improves the inverse kinematics problem for the 3D Romin Robot. By leveraging computer algebra techniques and the GES-GVW-CGS algorithm within the Maple software environment, we can efficiently analyze the parameter space and provide solutions for a wide range of robot configurations. This research expands the applicability of existing methods to complex robotic systems and showcases the power of computational tools in advancing robotics research and development.