As a common practice, a large hydro-generator will operate in leading phase conditions to absorb the reactive power of the power grid. However, the accurate and precise prediction of the leading phase operation capacity of a large hydro-generator has always been a formidable challenge to engineers and academicians because it is extremely hard to compute the eddy currents and losses as well as the local overheating in the pressure plate and finger. To address this problem, a full three dimensional (3D) finite element model and method of the coupled eddy current and temperature fields in the end region of a large hydro-generator are developed. The equivalent medium parameters used in the computations are comprehensively discussed. Moreover, some numerically based solution methodologies for accurate computation of the field and armature currents under different leading phase conditions are proposed. Numerical results on the coupled eddy current and temperature fields in the end regions of a 250 MW hydro-generator confirm positively the feasibility of the present work.