  The thermoelectric properties of the surface states in three-dimensional
topological insulator nanowires are studied. The Seebeck coefficients $S_c$ and
the dimensionless thermoelectrical figure of merit $ZT$ are obtained by using
the tight-binding Hamiltonian combining with the nonequilibrium Green's
function method. They are strongly dependent on the gate voltage and the
longitudinal and perpendicular magnetic fields. By changing the gate voltage or
magnetic fields, the values of $S_c$ and $ZT$ can be easily controlled. At the
zero magnetic fields and zero gate voltage, or at the large perpendicular
magnetic field and nonzero gate voltage, $ZT$ has the large value. Owing to the
electron-hole symmetry, $S_c$ is an odd function of the Fermi energy while $ZT$
is an even function regardless of the magnetic fields. $S_c$ and $ZT$ show
peaks when the quantized transmission coefficient jumps from one plateau to
another. The highest peak appears while the Fermi energy is near the Dirac
point. At the zero perpendicular magnetic field and zero gate voltage, the
height of $n$th peak of $S_C$ is $\frac{k_B}{e}\texttt{ln}2/(|n|+1/2)$ and
$\frac{k_B}{e}\texttt{ln}2/|n|$ for the longitudinal magnetic flux
$\phi_{\parallel} = 0 $ and $\pi$, respectively. Finally, we also study the
effect of disorder and find that $S_c$ and $ZT$ are robust against disorder. In
particular, the large value of $ZT$ can survive even if at the strong disorder.
These characteristics (that $ZT$ has the large value, is easily regulated, and
is robust against the disorder) are very beneficial for the application of the
thermoelectricity.
