A numerical study is presented to investigate the spin-dependent transport through poly(dG)-poly(dC) DNA molecule sandwiched between ferromagnetic contacts in the absence and in the presence of environmental effects. Making use of tight-binding procedure and within the framework of a generalized Green’s function technique, the room temperature current-voltage characteristics of DNA molecule and the giant magnetoresistance (GMR) of Electrode/DNA/Electrode structure, with iron (Fe) as the electrode are studied. It is found that the GMR to be lower than 12% for small applied bias and about 35% for applied bias larger than 2.5 volts. Considering the environmental effects, the GMR would be increased up to 13% at a bias lower than 2 volts and decreases up to 23% for the bias about 2.5 volts. In addition, our calculations indicate that for applied biases around 2.5 volts, the GMR decreases when the temperature increased.