This paper presents a new transient stability index based on the implicit expression for the stability region boundary and an approximation of the proposed index based on the quadratic approximation of the stability region. The proposed index may have no constraints such as the existence of Lyapunov-type energy function. Two applications， calculating the critical clearing time and contingency ranking， are presented based on the approximated index. The critical clearing time is obtained by the quadratic equation that fits the relation between the transient stability index and clearing time. The contingency ranking results are obtained directly by comparing the values of the transient stability index of different contingencies. Simulations in IEEE 3-machine 9-bus system and 10 machine 39-bus New England system show the applicability of the proposed transient stability index.