A new approach to solve the stability-constrained optimal power flow（SCOPF） based on a novel transient stability margin index and its sensitivities is proposed. The transient stability constraints represented by the differential-algebraic equations are converted to the inequality constraints of the transient stability margin index and its sensitivities with respect to the control variables in this approach. Furthermore the transient stability margin index is based on the implicit expression for the stability region boundary related to the controlling unstable equilibrium point（CUEP）， and can be approximated with quadratic approximation of the stability region. The converted SCOPF problem can be easily solved by the nonlinear programming approach， which not only takes a satisfied convergence， but also can deal with more anticipated faults simultaneously. Simulation results in the New England 10-generator 39-bus system show the effectiveness of the proposed approach.