In order to predict the punching shear capacity of slab-column connections more accurately, a new calculation method for punching shear capacity of slab-column connections was proposed based on the beam shear failure mechanism and modified compression-field theory (MCFT). Firstly, it was assumed that the punching load of reinforced concrete (RC) slab-column connections without shear reinforcement was jointly provided by the concrete in the upper shear compression zone, the aggregate interlock force in the cable-stayed zone, and the dowel action in the tension zone. Secondly, the different stress states of shear compression zone, cable-stayed zone, and tension zone were analyzed, and the shear bearing capacity calculation formulas of shear compression zone, cable-stayed zone, and tension zone were established respectively. Then, through statistical analysis and theoretical derivation, the calculation formulas of the heights of shear compression zone and compression zone, as well as the critical inclined crack angle were obtained. Finally, the contributions of the two parts of the punching resistance capacity were superimposed to establish the calculation method of punching shear capacity of RC slab-column connections without shear reinforcement. The calculation method was applied to predict the ultimate punching shear strength of 54 slab-column connections in relevant literature. Results show that the calculated values were in good agreement with the experimental values, and the variation coefficient was small. The proposed calculation method can be used to calculate the ultimate punching shear strength of RC slab-column connections without shear reinforcement.