We developed a novel metal-organic framework (MOF)@covalent-organic framework (COF) hybrid with a hierarchical nanostructure and excellent photoactivity, which further acted as the bifunctional platform of a dual-mode photoelectrochemical (PEC) and electrochemical (EC) biosensor for detecting HIV-1 DNA via immobilizing the HIV-1 DNA probe. First, the presynthesized Cu-MOF nanoellipsoids were used as the template for the in situ growth of the COF network, which was synthesized using copper-phthalocyanine tetra-amine (CoPc-TA) and 2,9-bis[p-(formyl)phenyl]-1,10-phenanthroline as building blocks through the Schiff base condensation. In view of the large specific surface area, abundant reserved amino group, excellent electrochemical activity, and high photoactivity, the obtained Cu-MOF@CuPc-TA-COF heterostructure not only can serve as the sensitive platform for anchoring the HIV-1 DNA probe strands but also can be utilized as the signal transducers for PEC and EC biosensors. Thereby, the constructed biosensor shows the sensitive and selective analysis ability toward the HIV-1 target DNA via the complementary hybridization between probe and target DNA strands. The dual-mode PEC and EC measurements revealed that the Cu-MOF@CuPc-TA-COF-based biosensor displayed a wide linear detection range from 1 fM to 1 nM and an extremely low limit of detection (LOD) of 0.07 and 0.18 fM, respectively. In addition, the dual-mode PEC-EC biosensor also demonstrated remarkable selectivity, high stability, good reproducibility, and preferable regeneration ability, as well as acceptable applicability, for which the detected HIV-1 DNA in human serum showed good consistency with real concentrations. Thereby, the present work can open a new dual-mode PEC-EC platform for detecting HIV-1 DNA based on the porous-organic framework heterostructure.