With the rapid development and diverse engineering applications of VSC-HVDC technology, development in power industry has put forward higher economic and security requirements for the security-constrained optimal power flow. Under these circumstances, this paper proposes a security-constrained optimal power flow model for hybrid AC/DC power grids that incorporates the VSC-HVDC corrective control. The linear relationship between the pre-contingency state power flow and post-contingency state power flow is established based on the shift factor and the reliability constraints are described as the linear inequality constraints of the post-contingency state active power flow which is expressed by the pre-contingency state branch power flow. With the inherent ability of the VSC-HVDC converter station (short as VSC station) to rapidly regulate active power taken into account, this paper utilizes the linear relationship between the active power adjustment of the VSC station and the power flows of transmission lines and electrical equipment and corrects the reliability constraints with the sensitivity coefficient. Hence the correction of the post-contingency state power flow is reflected in the constraints. By solving the proposed model with the primal-dual interior-point method, the pre-contingency state optimal security operating point that considers the corrective capability of the VSC stations is obtained. Finally, the correctness and validity of the proposed model is verified based on a VSC-HVDC modified IEEE 14-bus system.