Transient stability constrained optimal power flow (TSCOPF) is one of hot research issues of power system. It is divided into transient stability assessment, sensitivity analysis and OPF sub-problems to solve iteratively. Margin expressions under different conditions are given by EEAC equivalent. The margin sensitivities with regard to control variables are obtained by trajectory sensitivity, which constitute linear inequality constrains. The interior-point method is used to solve the stability constrained optimal power flow. Correction factor is used to avoid over-adjustment. In this way, power system can meet the given stability margin. This approach can consider multi-swing unstable problems and deal with multi-contingency problems under different unstable mode. Its effectiveness is validated on the IEEE 10-generator 39-bus system.