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Taking into account the electric field dependence of carrier mobility and permittivity, the current-voltage relationship dominated by space-charge-limited conduction for high dielectric constant ferroelectric thin films, consisting of (Ba, Sr)TiO3 and Pb(Zr, Ti)O3 is derived. Typical current-voltage characteristics are given by the derived relationship with empirical values for its parameters. The obtained current characteristics effectively account for the high-field current characteristics including the quasi-Ohmic region and the small power exponent law region in the electric field ranging from 106 V/cm to 107 V/cm observed experimentally in a very thin BaTiO3 single crystal in a previous study [Appl. Phys. Lett. 86 (2005) 152903].