We found that under pressure SnO with alpha-PbO structure, the same structure as in many Fe-based superconductors, e.g. beta-FeSe, undergoes a transition to a superconducting state for p > 6 GPa with a maximum Tc of 1.4 K at p = 9.3 GPa. The pressure dependence of Tc reveals a dome-like shape and superconductivity disappears for p > 16 GPa. It is further shown from band structure calculations that SnO under pressure exhibits a Fermi surface topology similar to that reported for some Fe-based superconductors and that the nesting between the hole and electron pockets correlates with the change of Tc as a function of pressure.