The Hall mobility of electrons in n-type germanium at high electric fields is studied, taking into consideration the ellipsoidal many-valley band structure. The distribution function of carriers in a many-valley semiconductor is first obtained assuming acoustic phonon, optical phonon and intervalley scattering. Expressions for Hall mobility are then derived using this distribution function and numerical computations made with the parameter values of n-type germanium. It is found that (i) the Hall mobility is anisotropic, (ii) its value is a maximum when the electric field is applied in the <100> direction, and (iii) its value is a minimum when the electric field is in the <111> direction. It is also found that the anisotropy factor is independent of the value of the electric field for predominant acoustic phonon scattering, but depends on the field for predominant optical and intervalley scattering.