The influence of ambient current fields on the mild-slope approximation is reassessed using the Hamiltonian variational principle. Considering the slowly modulated non-uniform currents which may possess both vertical and horizontal variations, the extended mild-slope equation for surface waves propagating over slowly varying topography is derived. It is found that for large current velocities comparable to the wave celerity and the group velocity?the extended mild-slope equation is valid. For the validity of the geometric optics-approximation, additional conditions concerning current fields should be satisfied. The influence of ambient current fields on the mild-slope approximation is reassessed using the Hamiltonian variational principle. Considering the slowly modulated non-uniform currents which may possess both vertical and horizontal variations, the extended mild-slope equation for surface waves propagating over slowly varying The is found that for large current velocities comparable to the wave celerity and the group velocity? the extended mild-slope equation is valid. For the validity of the geometric optics-approximation, the additional conditions concerning current fields should be satisfied.