The magnetic-flux-dependent dispersions of sub-bands in topologically protected surface states of a topological insulator nanowire manifest as Aharonov-Bohm oscillations (ABOs) observed in conductance measurements, reflecting the Berry's phase of π because of the spin-helical surface states. Here, we used thermoelectric measurements to probe a variation in the density of states at the Fermi level of the surface state of a topological insulator nanowire (Sb-doped Bi₂Se₃) under external magnetic fields and an applied gate voltage. The ABOs observed in the magnetothermovoltage showed 180° out-of-phase oscillations depending on the gate voltage values, which can be used to tune the Fermi wave number and the density of states at the Fermi level. The temperature dependence of the ABO amplitudes showed that the phase coherence was kept to T = 15 K. We suggest that thermoelectric measurements could be applied for investigating the electronic structure at the Fermi level in various quantum materials.