A steam generator and a cooking apparatus having a steam generator are provided. The steam generator may include a steam generation tube; an inflow tube configured to provide a passage so that water is introduced into the steam generation tube; at least one heater disposed on an outer surface of the steam generation tube to heat the water and generate steam; a discharge tube disposed above the steam generation tube to provide a passage so that the steam is discharged; and an adaptor unit configured to branch discharge water and the steam discharged from the discharge tube. The discharge tube may have an inner diameter that gradually increases in an upward direction.