To investigate a complex physical phenomenon and its evolution law at the cathode surface at the initial stage of the explosive electron emission process in a high-power diode, in this paper we present a model of a planar vacuum diode with a field emission cathode. The model is one-dimensional and nonstationary. To study the space charge effect of the emitted electrons on the electric field at the cathode surface, Poisson's equation is solved numerically by using our developed code, and the time-dependences of the electric field at the cathode surface for different cases are obtained. The results show that the electric field at the cathode surface first oscillates and finally yields a steady state. The absolute value of the steady electric field at the cathode surface is higher for the higher field enhancement factor at a given applied electric field, and the applied electric field has the same effects on the steady value at a certain field enhancement factor. The electric field at the cathode surface completely determines the extracted field emission current density from the cathode, and at the same time, the electric field at the cathode surface is influenced by the emitting current density.