The grading capacitor (GC) of circuit breaker (CB) is one of the most cost-effective methods to suppress secondary arc. Taking the double-break CB as an example, its topology is briefly introduced. The electric circuit for power system with GC is then established. From the perspective of minimizing secondary arc current, the formula for the capacitance of GC is deduced according to the Kirchhoff's voltage law. Based on the equal-area criterion, the transient process of power angle and speed of generator in the event of fault is investigated, and the role of GC in the transient stability is quantitatively investigated. Meanwhile, the expressions for the accelerating and decelerating areas are computed through the numerical calculus, and the impact of GC capacitance on the critical clearing time (CCT) is discussed. Furthermore, to verify the aforementioned analysis, a model is established in the environment of MATLAB/Simulink, and two cases are considered, i.e., a single machine infinite bus (SMIB) power system and a multi-machine power system. Both the theoretical analysis and the simulation results demonstrate that the use of GC can strength the electrical connection between two remote power sources, undermines the oscillating amplitude of power angle, and shorten the attenuation duration. As a result, the CCT and transient margin would be increased. In other words, we can prong the dead time and guarantee the successfulness for autoreclosure scheme. The GC of CB is much superior to the existing four-legged shunt reactor and high speed grounding switch in addressing the secondary arc issue.