The origin and formation mechanism of a submerged vortex and an air-entraining vortex have been fully clarified by large-eddy simulation (LES) that used approximately 2 billion hexahedral elements with maximum resolution of 0.255 mm and was applied to the internal flows of a model pump sump. The model pump sump is composed of a 2,500 mm-long water channel of rectangular cross section with a width of 300 mm and a water depth of 100 mm and a vertical suction pipe with a 100 mm diameter installed at its downstream end with an offset of 10 mm from the centerline of the rectangular channel. At the upstream end of the channel, a uniform velocity of 0.37 m/s is given. LES with different wall boundary conditions have revealed that the origin of a submerged vortex is the mean shear of the approaching boundary layers that develop on the bottom and side walls of the pump sump. From detailed investigations of LES computed for a long time period of 16 seconds have revealed that deviation of the mean flow that approaches the suction pipe triggers conversion of the axis of the vorticity that was originally aligned to the lateral direction in the approaching boundary layers to that aligned to the vertical direction. The local acceleration of the vertical flow stretches the afore-mentioned vertical vortex, which results in formation of a submerged vortex. The separated flows downstream of the suction pipe generate vertical vorticity, and forms an air-entraining vortex when such a vortex is sucked into the suction pipe. Computations with a different bellmouth height and a different water-surface height have supported the above mentioned origin and formation mechanism of these vortices.