The electronic structure of tungsten tip of (111) surface under external electric fields is studies by using discrete variational-local density functional method. The tunneling orbitals(TOs) and the charge distributions of the tip are calculated and analysed in detail under different conditions. The results show that the components of TOs are sensitive to the polarity, amplitude of the external electric field and the distances between tip and sample. It is found that although 5dz2 has some contribution to TOs, it is not dominant, which differs from the previous theoretical calculations. The dominating contributions are from 5dxz and 5dyz orbitals under positive bias voltages. However, under negative bias voltages, TOs are made of many orbitals including 6s orbital. Our results can explain the phenomenon in STM experiments that the resolution of STM images will be changed using the same tip when the polarity of the electric field is reversed, and can also predict that if one uses tungsten tip of (111) surface, the inverted STM images should be observed.