Recently, some studies showed that the GeV gamma-ray excess signal from the central Milky Way can be explained by the annihilation of ~ 40 GeV dark matter through the bbar b channel. Based on the morphology of the gamma-ray flux, the best-fit inner slope of the dark matter density profile is γ = 1.26. However, recent analyses of the Milky Way dark matter profile favor γ = 0.6 – 0.8. In this article, we show that the GeV gamma-ray excess can also be explained by the Sommerfeld-enhanced dark matter annihilation through the bbar b channel with γ = 0.85 – 1.05. We constrain the parameters of the Sommerfeld-enhanced annihilation by using data from Fermi-LAT. We also show that the predicted gamma-ray fluxes emitted from dwarf galaxies generally satisfy recent upper limits on gamma-ray fluxes detected by Fermi-LAT. Copyright © 2016 National Astronomical Observatories, Chinese Academy of Sciences and IOP Publishing Ltd.