Transient stability constrained optimal power flow (TSCOPF) is able to effectively coordinate the dynamic security and operation economics for power systems. Focusing on existing technical difficulties, including low computational efficiency and high memory consumption, this paper proposes an active-set reduced-space sequential quadratic programming algorithm to solve this problem. This approach is able to take advantage of the characteristics of few degree of freedom in TSCOPF problems, in order to decrease the computational complexity. Meanwhile, active-set technique is introduced to reduce the dimensions of quadratic programming subproblems by filtering inactive inequality constraints and reducing computational demand. Compared with existing algorithms, case studies based on a series of test cases indicate the effectiveness of the proposed approach in solving TSCOPF problems for large-scale power systems.