Thermoelectric transport in topological insulators (TIs) is theoretically studied. TIs have gapless edge states in two dimensions, and do surface states in three dimensions. Both of the states have backscattering-free nature, and they remain gapless in the presence of nonmagnetic impurities. In particular, the edge states in two-dimensional TIs form perfect conducting channels. In this study, we calculate system-size dependence of thermoelectric properties in two-dimensional TIs, and evaluate the inelastic scattering length of the edge states by phonons, which affects the thermoelectric properties sensitively. We also study thermoelectric transport in three-dimensional (3D) TIs and compare with two dimensions. In both two-and three-dimensional TIs, there is a competition between the surface/edge and bulk transports in the thermoelectric phenomena. The surface transport in 3D TIs is relatively weak compared with the bulk transport due to impurities. Furthermore, we also study gapped 3D TIs in thin slab geometry and show large values of the figure of merit in the gapped system. This result is consistent with the previous work.