We have studied the triplet energy transfer (TET) for photosynthetic light-harvesting complexes, the bacterial light-harvesting complex II (LH2) of Rhodospirillum molischianum and Rhodopseudomonas acidophila, and the peridinin chlorophyll a protein (PCP) from Amphidinium carterae. The electronic coupling factor was calculated with the recently developed fragment spin difference scheme (You and Hsu, J. Chem, Phys. 2010, 133, 074105), which is general computational scheme that yields the overall coupling under the Hamiltonian employed. The TET rates were estimated based on the couplings obtained. For all light-harvesting complexes studied, there exist nanosecond triplet energy transfer from the chlorophylls to the carotenoids. This result supports a direct triplet quenching mechanism for the photoprotection function of carotenoids. The TET rates are similar for a broad range of carotenoid triplet state energy, which implies a general and robust TET quenching role for carotenoids in photosynthesis. This result is also consistent with the weak dependence of TET kinetics on the type or the number fa conjugation lengths in the carotenoids and their analogues reported in the literature. We have also explored the possibility of forming triplet excitons in these complexes. In B850 of LH2 or the peridinin cluster in PCP, it is unlikely to have triplet exciton since the energy differences of any two neighboring molecules are likely to be much larger than their TET couplings. Our :results provide theoretical limits to the possible photophysics in the light-harvesting complexes.