As an important QED effect to detect the vacuum polarization, birefringence in the presence of a strong electric and magnetic field, E0⊥ B0, E0≤ c B0, is considered. The directional dependence of birefringence is obtained. In two special cases: E0= 0 and E0= c B0, our results are consistent with the previous ones. The refractive index of the probe wave propagating in the -E0× B0 direction decreases with E0/c B0, while that in the-E0× B0 direction increases with E0/c B0.The physics of the direction dependence of birefringence maybe the E0× B0 drift velocity of the virtual electrons and positrons. As an important QED effect to detect the vacuum polarization, birefringence in the presence of a strong electric and magnetic field, E0⊥ B0, E0 ≦ c B0, is considered. 0 and E0 = c B0, our results are consistent with the previous ones. The refractive index of the probe wave propagating in -E0 × B0 direction decreases with E0 / c B0, while that in the -E0 × B0 direction increases with E0 / c B0. The physics of the direction dependence of birefringence maybe the E0 × B0 drift velocity of the virtual electrons and positrons.