We investigated the effect of band gap engineering on the thermoelectric properties of n-type Cu0.008Bi2Te3 using the two-band (TB) model. The experimental measurements showed a zT of ~0.41 at 300 K and ~0.46 at 520 K, with an optical band gap of ~0.13 eV. While fixing the density-of-state effective mass (md *), deformation potential (Edef), lattice thermal conductivity (κl), and Fermi level based fitted based on experimental data, we varied the band gap (Eg) from 0.1 to 0.3 eV to analyze its impact on the thermoelectric performance. The TB model calculations revealed that the power factor (PF) increased and the thermal conductivity (κ) decreased with increasing Eg at both 300 K and 520 K, leading to an enhancement in zT. The magnitude of this enhancement was more pronounced at 520 K than at 300 K, which can be attributed to the suppressed bipolar effects at higher temperatures. Our findings suggest that increasing the band gap of Cu0.008Bi2Te3 can significantly improve its thermoelectric performance, to an estimated maximum zT of ~0.61 at 520 K for Eg = 0.3 eV. The theoretical maximum zT, considering the optimized hole concentration (nH), was estimated to be ~0.75. We demonstrate that Eg engineering of narrowbandgap semiconductor thermoelectric materials can significantly enhance thermoelectric performance.