The galaxy pairwise velocity dispersion (PVD) can provide important tests of non-standard gravity and galaxy formation models. We describe measurements of the PVD of galaxies in the Galaxy and Mass Assembly (GAMA) survey as a function of projected separation and galaxy luminosity. Due to the faint magnitude limit (r < 19.8) and highly complete spectroscopic sampling of the GAMA survey, we are able to reliably measure the PVD to smaller scales (r⊥ = 0.01 h -1 Mpc) than previous work. The measured PVD at projected separations r⊥ < 1 h -1 Mpc increases near monotonically with increasing luminosity from σ12 ≈ 200 km s-1 at Mr = -17 mag to σ12 ≈ 600 km s-1 at Mr ≈ -22 mag. Analysis of the Gonzalez-Perez et al. (2014) GALFORM semi-analytic model yields no such trend of PVD with luminosity: the model overpredicts the PVD for faint galaxies. This is most likely a result of the model placing too many low-luminosity galaxies in massive haloes.