A novel scheme is proposed to realize the electrostatic surface trapping of cold polar molecules on a chip by using a square charged wire. The spatial distribution of the electrostatic field around the square charged wire is calculated. Then the dependent relation between the position of trapping center and the geometric parameters is analyzed. Afterwards, the dependences of the electric field distribution (including the corresponding Stark trapping potential for CO molecules) on the geometric parameters of the square wire is studied in the x and z direction. The study shows that the efficient trapping potential for CO molecules is greater than 130 mK, which is high enough to trap cold polar molecules with a temperature of 50 mK in the weak-field-seeking states. Obviously, the electrostatic surface trapping proposed here has some important applications in the fields of molecular optics and molecular chip, quantum optics, quantum computing and quantum information processing, etc.