Narrow-bandgap thermoelectric semiconductors with precisely designed electronic structures are required for highly efficient energy-recycling societies. As a solution to the underestimation of the bandgap value, which is the most serious problem of first-principles calculations based on the density functional theory (DFT) especially for narrow-gap materials, we consider the PBE0 functional, Heyd–Scuseria–Ernzerhof screening hybrid functional (HSE06), and recently developed Gaussian–Perdew–Burke–Ernzerhof (Gau–PBE) hybrid functional. The convergence of the energy and bandgap of extremely narrow-gap semiconductor α-SrSi2 with respect to the mesh parameters, which are the number of k-point divisions in DFT and Hartree–Fock (HF) exchange integral calculations, was investigated using each functional, and the electronic structure and transport properties were then calculated. Consequently, Gau–PBE provided similar electronic and transport properties to those obtained using the other methods while lowering the calculation costs, i.e., with >80% less computation time and a smaller number of HF mesh points. These results provide insights to the low-cost practical calculation of the precise transport properties of low-temperature thermoelectric materials.