The structural, electronic, magnetic, and thermoelectric properties of half-Heusler alloys ZrCo1-XFeXSb (X = 0, 0.25, 0.5, 0.75, 1) are investigated using the density functional theory. It is evident that ZrCoSbis a non-magnetic semiconductor. This study investigates the influence of substituting Fe for Co on the electronic structure and magnetic characteristics of ZrCoSb. The alloys transform into half-metallic ferromagnets as Fe substitutes Co. The indirect band gap of the ZrCo1-XFeXSb alloys decreases with increasing Fe content. The phonon dispersion curve is studied to determine the structural stability. The calculated values for the elastic constant for each composition satisfy the criteria for mechanical stability. To analyse its thermoelectric properties, the semi-classical Boltzmann transport theory is used to determine the Seebeck coefficients, electrical and thermal conductivities, and power factor as a function of temperature.