We investigate theoretically the thermoelectric and thermal transport properties of graphene under strong magnetic field in the presence of short-range scatterers. The numerical results are in good agreement with available experimental data for all thermoelectric quantities except for the Seebeck coefficient near zero chemical potential. This anomaly is attributed to the overestimation of the longitudinal resistivity. Furthermore, we find an anomalous oscillation in the transverse thermal conductivity at the lowest Landau level and double peaks in the longitudinal thermal conductivity at higher Landau levels, which are expected to be observed in future experiments on high mobility graphene samples. An important finding of our work is that the thermoelectric figure of merit ZT can be as high as 2.4 for a magnetic field under which the chemical potential is pinned to the [n=1] Landau level. This finding can greatly advance the thermoelectric application of graphene
