Nonequilibrium electronic transport through a quantum dot coupled to ferromagnetic leads (electrodes) is studied theoretically by the nonequilibrium Green function technique. The system is described by the Anderson model with arbitrary correlation parameter U . Exchange interaction between the dot and ferromagnetic electrodes is taken into account via an effective molecular field. The following situations are analyzed numerically: (i) the dot is symmetrically coupled to two ferromagnetic leads, (ii) one of the two ferromagnetic leads is half-metallic with almost total spin polarization of electron states at the Fermi level, and (iii) one of the two electrodes is nonmagnetic whereas the other one is ferromagnetic. Generally, the Kondo peak in the density of states (DOS) becomes spin-split when the total exchange field acting on the dot is nonzero. The spin-splitting of the Kondo peak in DOS leads to splitting and suppression of the corresponding zero bias anomaly in the differential conductance.