The manipulation of topological architectures in two-dimensional (2D) covalent organic framework (COF) materials for different applications is promising but remains a great challenge. Here, we first report the topology-selective synthesis of two distinct varieties of 2DCOFs, imine-based HT-COFs and benzimidazole-fused BI-HT-COFs, by simply altering acid catalysts. To HT-COFs, a superlattice of 1D channel with a persistent triangular shape is formed via Schiff base reaction, while to BI-HT-COFs, a hexagonal lattice structure with a highly conjugated structure and imidazole linkages is constructed due to an imine-based cyclization reaction. The two COFs exhibited marked differences in their bandgap, chemical stability, molecular adsorption, and catalytic activity, which make them have different fields of application. This work not only diversifies the hexaaminotriphenylene-based 2DCOF topologies but also provides vivid examples of structure-property relationships, which would facilitate fundamental research and potential applications of 2DCOFs.