Deep mining is an inevitable trend in China and the world, for which the construction of deep and large vertical shafts is the primary task. A shaft sinking headframe is a basic structure for supporting various hoisting and sinking equipment during vertical shaft construction. The design of the shaft sinking headframe is challenging due to the significant differences in the geometry and working load compared to conventional steel structures. Recently, the effect of uneven foundation settlement on the shaft sinking headframe has been of great concern when sinking shafts by the freezing sinking method or in permafrost soil areas. In this study, finite element calculations were performed to investigate the mechanical behavior of the SA-3 shaft sinking headframe under uneven foundation settlement (0.001–0.006 L) and normal working-load conditions. The results indicate that the most unfavorable condition for the stress of members is the diagonal double foundation settlement, and in the view of the geometric offset, the most unfavorable condition is the same-side double foundation settlement. The corner members near the settled foundation were changed from a state of compression to tension. Uneven foundation settlement of less than 0.001 L is acceptable for the safety and service performance of the shaft sinking headframe. These criteria can be used for reference in engineering practice.