As the key part of formulating a generation schedule, the Security-Constrained Unit Commitment (SCUC) problem is of vital importance in the optimizated operation of a power system. The SCUC problem has a large number of constraints and is thereby difficult to solve. We propose a constraint reduction method based on an auxiliary optimization problem. First, the auxiliary optimization problem related to a specific post-contingency security constraint is introduced, so that a sufficient and necessary condition for identifying redundant constraints can be established. Then, three acceleration methods for the identification process are introduced, including relaxing the auxiliary optimization problem, proposing a feasible criterion for pre-classification of post-contingency security constraints, and introducing multithread parallel computing. Finally, the effectiveness and correctness of the proposed method are verified on the simulation of IEEE118 test system. This work is supported by the National Key Research and Development Program of China (No. 2017YFB0902800) and the Science and Technology Project of China Southern Power Grid (No. GDKJXM20190139).