Compared to traditional manipulators, cable-driven hyper-redundant manipulators (CDHRMs) have advantages such as remote drive, compact size, and multiple degrees of freedom, enabling flexible operation in narrow and complex environments. They are widely used in hazardous industrial settings. These manipulators use motors to drive steel cables, creating a mapping not only between the operational space (OS) and joint space (JS) but also between the cable-driven space (CDS) and JS. Due to the high coupling between the drive cables, solving this relationship analytically becomes overly complex. This paper proposes a forward kinematics (FK) solution method for CDHRMs based on the self-attention mechanism (SAM). The method leverages the SAM to identify relationships between cables across different joints as well as among different cables within the same joint. It allows for direct calculation of the manipulator’s end position from cable lengths, achieving end-to-end output and improving convenience and computational efficiency. Finally, an 8-joint CDHRM was used as the experimental object, and simulation data were collected as experimental validation inputs into the network. The results show that the average end position error of the manipulator's final joint is 1.514 cm, verifying the effectiveness of the method.