For slab-column connections subjected to vertical loads and unbalanced bending moments, the unbalanced bending moment is typically equated to vertical loads in most existing methods for calculating their punching capacity. However, there is significant controversy regarding the calculation of the unbalanced bending moment ratio coefficient in existing methods, and the coupling effect between vertical loads and unbalanced bending moments has not been adequately considered. Therefore, this paper first proposes a new equation for calculating the punching capacity of slab-column connections under vertical loads only and validates it through comparison with experimental results. Additionally, a novel equation for calculating the flexural capacity of slabs under unbalanced bending moments is proposed. Based on experimental results and considering the bending-shear correlation, an equation for calculating the punching capacity of slab-column connections under the combined action of vertical loads and unbalanced bending moments is then derived. Finally, the proposed method is compared with various design code methods. The results indicate that the proposed method can more accurately predict the punching capacity of slab-column connections.