We investigate the spin polarized current through a quantum dot connected to ferromagnetic leads in the presence of a finite spin-dependent chemical potential. The effects of the spin polarization of the leads p and the exteal magnetic field B are studied. It is found that both the magnitude and the symmetry of the current are dependent on the spin polarization of the leads. When the two ferromagnetic leads are in parallel configuration, the spin polarization p has an insignificant effect on the spin current, and an accompanying charge current appears with the increase of p. When the leads are in antiparallel configuration, however, the effect of p is distinct. The charge current is always zero regardless of the variation of p in the absence of B. The peaks appearing in the pure spin current are greatly suppressed and become asymmetric as p is increased. The applied magnetic field Bresults in an accompanying charge current in both the parallel and antiparallel configurations of the leads. The characteristics of the currents are explained in terms of the density of states of the quantum dot.