To address the demand for memory scaling capabilities, three-dimensional integrated circuits (3D-ICs) based on short and dense through-silicon vias (TSVs) have been introduced. However, the defects of TSVs considerably influence the yield and reliability of 3D-ICs. For this reason, TSV repair using switch matrix topology (TRUST) is proposed in this paper. TRUST adopts a switch matrix, which has a high routing flexibility, to realize TSV connections. Consequently, a 100% repair rate can be achieved for the 3D-ICs that have faulty TSVs smaller than or equal to redundant TSVs. Furthermore, TRUST utilizes content-addressable memories in built-in self-repair to identify TSV repair paths via a simple TSV repair path search algorithm. For this reason, TRUST can be applied to repair manufacturing and aging defects of TSVs. Nevertheless, TRUST can be applied with reasonable area and delay overheads, such as 58.3% area reduction and 55.1% delay reduction compared to the only conventional TSV repair architecture that can achieve the optimal repair rate. In addition, the area ratios in high bandwidth memory (HBM) and HBM2 are only 5.3% and much smaller than 0.1%, respectively. The advantages are experimentally verified.