While an intense electron beam passes through the accelerating gaps of a linear induction accelerator, a strong wake field will be excited. In this paper a relatively simple model is established based on the interaction between the transverse magnetic wake field and the electron beam, and the numerical calculation in succession generates a magnetic wake field distribution along the accelerator and along the beam pulse as well. The axial electric wake field is derived based on the relation between field components of a resonant mode. According to some principles in existence, the influence of this field on the high voltage properties of the induction gap is analyzed. The Dragon-I accelerator is taken as an example, and its maximum electric wake field is about 17 kV/cm, which means the effect of the wake field is noticeable.