The Seebeck effect and the Nernst effect, which reflect the appearance of electric fields along x -axis and along y -axis ( E x and E y ), respectively, induced by the thermal gradient along x -axis, are studied in the QGP at an external magnetic field along z -axis. We calculate the associated Seebeck coefficient ( S xx ) and Nernst signal ( N ) using the relativistic Boltzmann equation under the relaxation time approximation. In an isotropic QGP, the influences of magnetic field ( B ) and quark chemical potential ( μ q ) on these thermoelectric transport coefficients are investigated. In the presence (absence) of weak magnetic field, we find S xx for a fixed μ q is negative (positive) in sign, indicating that the dominant carriers for converting heat gradient to electric field are negatively (positively) charged quarks. The absolute value of S xx decreases with increasing temperature. Unlike S xx , the sign of N is independent of charge carrier type, and its thermal behavior displays a peak structure. In the presence of strong magnetic field, due to the Landau quantization of transverse motion of (anti-)quarks perpendicular to magnetic field, only the longitudinal Seebeck coefficient ( S zz ) exists. Our results show that the value of S zz at a fixed μ q in the lowest Landau level (LLL) approximation always remains positive. Within the effect of high Landau levels, S zz exhibits a thermal structure similar to that in the LLL approximation. As the Landau level increases further, S zz decreases and even its sign changes from positive to negative. The computations of these thermoelectric transport coefficients are also extended to a medium with momentum-anisotropy induced by initial spatial expansion as well as strong magnetic field.