Considering electron-impurity and electron-phonon scattering, we present a balance-equation-based theoretical examination of thermoelectric power (TEP) in a two-dimensional single-layer graphene away from the carrier neutrality point. Both the boundary scattering and phonon-phonon interaction in phonon relaxation processes are taken into account. We find that, at temperatures T > 10 K, the contribution to TEP mainly comes from diffusive processes and the phonon-drag effect can be ignored. However, at T ≤ 10 K, the phonon-phonon interaction leads to a phonon-drag peak in the temperature dependence of TEP. We also compare our results with experiments.