Detailed structures and thermoelectric (TE) properties are investigated for the perovskite La1-xSrxCoO3 and La1-xSrxCoO3 with 0 <= x <= 0.3. The monoclinic crystal structures for all samples are refined from powder X-ray diffraction, which reveals that the La1-xSrxCoO3 series has smaller global distortions but larger local distortions. The different structural distortions strongly influence the transport and TE properties in terms of resistivity, thermopower, thermal conductivity, bandwidth, and effective mass as well as electronic correlation. These results unambiguously demonstrate a close correlation between the structural distortions and TE characteristics in this family. Furthermore, a new approach is suggested to improve the TE performance by controlling the structure factors in such strongly correlated oxide systems. The effects of the spin-state transition of Co ions on the TE properties are also discussed.