The surface potential of the liquid-vapor interface of water plays a critical role in electrochemistry, interfacial reactivity, and solvation thermodynamics. However, direct experimental measurement of the surface potential of pure water is exceedingly challenging. Here we present a methodology to explore the effect of external electric field on the water surface potential. The methodology contains constant electrostatic potential molecular dynamics simulation [J. Chem. Phys., 126, 084704(2007)], in which, the electrode charges are allowed to fluctuate to keep the potential fixed, as well as a recently developed probe and average method [J. Phys.: Cond. Matter, 28, 464006(2016)] to accurately map out the electrostatic potential across the water surfaces. The methodology is applied to the coexistence of the vapor phase and the liquid phase of the room temperature pure water (described by a simple SPC/E water model) under different magnitudes of E-fields generated from the nearby electrodes, yielding a first-time calculation of the external E-field dependent water surface potential profiles, and the relationship between the water surface potential and the external E-field strength which has been rarely reported. We found an asymmetric effect of external E-field on the surface potential, i.e., the surface potential decreases with increasing the external E-field strength for the water surface close to the cathode, while the surface potential increases with increasing field strength for the surface close to the anode. The water surfaces are also characterized by calculating the number density and dipole polarization density profiles, which depict the presence of the external E-fields induced bulk polarization under high strength field. By comparing the dipole polarization density profiles and the potential profiles, we conclude that the asymmetric effect of external E-field on the surface potential is due to the asymmetric behavior in surface polarization under external E-field for the water surfaces near cathode or anode, and is also due to the polarization within bulk part of the liquid water. The methodology presented in the current study can be easily applied to more advanced water models such as polarizable water models which are beyond the SPC/E used in current work. The achievement of the fundamental data and the physics relationship between the surface potential of water and the applied external E-field could potentially facilitate the advancements in electrodynamics and thermodynamics of the liquid-vapor interfaces.