This study presents a comprehensive geometric modeling and error propagation analysis for a 3-degrees-of-freedom spindle head, focusing on an over-constrained parallel mechanism. Four geometric error models are established for the over-constrained spindle head, each considering different combinations of constraint wrenches. A set of sensitivity indices is formulated to evaluate the effectiveness of these models. Comparative sensitivity analysis suggests that a model incorporating all constraint wrenches is suitable for error propagation analysis. Two error propagation indices are introduced to quantify the impact of the geometric source errors on the position and orientation of an individual limb structure. The coupled error propagation indices account for the kinematic interactions among limb structures, allowing for a detailed analysis of the spindle head’s terminal accuracy. The relative deviations of error propagation indices are utilized to assess the quantitative impact of kinematic interactions on the geometric errors of an individual limb structure. Furthermore, this study analyzes the cumulative effects of kinematic errors from three limb structures to reflect the influence of kinematic interactions on the terminal accuracy of the spindle head. The findings indicate that geometric errors of the limbs in such an over-constrained spindle head are mutually compensatory, reducing linear and angular errors and enhancing the spindle head’s terminal accuracy.