Utilizing the first-principle calculations combined with Boltzmann transport equation (BTE) and semiclassical analysis, we have systematically investigated the electronic structure, lattice thermal conductivity κL, Seebeck coefficient S, and the dimensionless figure of merit zT as a function of hydrostatic pressure P in crystalline skutterudites CoSb3 and IrSb3. Interestingly, as the pressure increases, the band gap and κL show an approximate parabolic trend, which results in extraordinarily high S and excellent thermoelectric properties, and zT even exceeds 1.4(1.09) in IrSb3(CoSb3) at 54(58) GPa. This anomalous behavior arises from the electron distribution and intrinsic scattering processes. Further analyses indicate that (i) nonbonding electron pairs of Sb atoms are gradually transferred to the region between Co(Ir) and Sb atoms as the pressure increases, which leads to the formation of a partial metallic bond and thus the band gap first expands and then shrinks; (ii) the change of the strength of the anharmonic phonon scattering process results in the variation of κL. As a result, these behaviors cause excellent thermoelectric properties. Our results provide insight into the thermal transport properties of skutterudites, meanwhile, forecast potential high pressure applications for thermoelectric materials.