A model for the experimental results of the periodic oscillation of the electric field, so-called the electric field pulsation, observed in the Compact Helical Device (Fujisawa et al 1998 Phys. Rev. Lett.81 2256) and the Large Helical Device (Shimizu et al 2010 Plasma Fusion Res.5 S1015) is presented. A self-generated oscillation of the radial electric field is shown as the simulation result in helical plasmas. The reduction of the anomalous transport diffusivity in the core region is observed due to the strong shear of the radial electric field when the positive electric field is shown in the core region in the periodic oscillation of Er. Two different time scales are found in the self-generated oscillation, which are the transport time scale and the fast time scale at the transition of the radial electric field. This oscillation because of the hysteresis characteristic is attributed to the electric field pulsation observed in helical plasmas. The parameter region of the condition for the self-generated oscillation is derived. It is shown that the multiple solutions of the radial electric field for the ambipolar condition are necessary but not sufficient for obtaining the self-generated oscillation.