Band engineering is one of the effective approaches for designing ideal thermoelectric materials. Introducing an intermediate band in the band gap of semiconducting thermoelectric compounds may largely increase the carrier concentration and improve the electrical conductivity of these compounds. We test this hypothesis by Pb doping in Zintl Ca₅In₂Sb₆. In the current work, we have systematically investigated the electronic structure and thermoelectric performances of substitutional doping with Pb on In sites at a doping level of 5% (0.2 e per cell) for Ca₅In₂Sb₆ by using density functional theory combined with semi-classical Boltzmann theory. It is found that in contrast to Zn doping, Pb doping introduces a partially filled intermediate band in the band gap of Ca₅In₂Sb₆, which originates from the Pb s states by weakly hybridizing with the Sb p states. Such an intermediate band dramatically increases the electrical conductivity of Ca₅In₂Sb₆ and has little detrimental effect on its Seebeck coefficient, which may increase its thermoelectric figure of merit, ZT. Interestingly, a maximum ZT value of 2.46 may be achieved at 900 K for crystalline Pb-doped Ca₅In₂Sb₆ when the carrier concentration is optimized. Therefore, Pb-doped Ca₅In₂Sb₆ may be a promising thermoelectric material.