The phonon-drag thermopower is studied in a monolayer graphene on a piezoelectric substrate. The phonon-drag contribution [Formula: see text] from the extrinsic potential of piezoelectric surface acoustic (PA) phonons of a piezoelectric substrate (GaAs) is calculated as a function of temperature T and electron concentration n s. At a very low temperature, [Formula: see text] is found to be much greater than [Formula: see text] of the intrinsic deformation potential of acoustic (DA) phonons of the graphene. There is a crossover of [Formula: see text] and [Formula: see text] at around ~5 K. In graphene samples of about  >10 µm size, we predict S (g) ~ 20 µV at 10 K, which is much greater than the diffusion component of the thermopower and can be experimentally observed. In the Bloch-Gruneisen (BG) regime T and n s dependence are, respectively, given by the power laws [Formula: see text] ([Formula: see text]) ~ T (2)(T (3)) and [Formula: see text], [Formula: see text] ~ [Formula: see text]. The T(n s) dependence is the manifestation of the 2D phonons (Dirac phase of the electrons). The effect of the screening is discussed. Analogous to Herring's law (S (g) μ p ~ T (-1)), we predict a new relation S (g) μ p ~ [Formula: see text], where μ p is the phonon-limited mobility. We suggest that the n s dependent measurements will play a more significant role in identifying the Dirac phase and the effect of screening.