According to the theories of mathematics and physics,the research into the electrostatic field near by the sharp-point conductor surface has been proceeded.The electrical potential distribution and the equation of equipotential line are given.Making use of the relationship of electrical field intensity and the electrical potential,duduce the mathematic expression of electrical field intensity and superficial charge density has been deduced,making use of the software package facility of Mathematica5.0,equipotential line maps is plotted.