A pump has a shaft, an impeller arranged on the shaft, and a labyrinth seal which is arranged between stationary and moving parts of the pump. A plurality of blades are arranged on the rotor and a labyrinth seal extends at least between the shaft and a rear portion of the blades. A gap in the labyrinth seal is designed such that liquid water can be actively carried away, with the labyrinth seal for this purpose being designed at least in places with a channel in the form of a spiral and/or a staircase. The invention also relates to a fuel cell system having such a pump.