This paper presents the FEM analysis on the contact behavior characteristics of mechanical face seals in a small hydro-power turbine. Especially, the axial displacement and contact normal stress between a seal ring and a seal seat of a primary sealing unit have been analyzed as functions of rotating speed of a hydro-turbine, sealing gap, water and cooling fluid temperature. Those are strongly related to a leakage of water and wear between a seal ring and a seal seat. The FEM computed results present that the rotating speed of a hydro-turbine may be kept less than 800 rpm, and the sealing gap in a primary sealing unit is restricted $0.5~5$. The coolant temperature in which is most influential parameter to the contact behaviors of a sealing unit may be kept less than $15^{circ}C$ for a safe operation of a sealing unit without a leakage and wear.