The electrostatic system consisting of two uniformly charged identical rings and an infinite grounded conductor circular cylinder is studied. δ function is used to express the volume density function of the line charges in cylindrical coordinates．The Poisson equation with boundary condition is changed into Laplace equation and solved exactly.The potential distribution of the system is analyzed．The induced surface charge density on the inner surface of the cylinder is obtained from the potential distribution．The electric field produced by the induced charge along the axis of the system is calculated．It is found that because of the influence of the induced charge, the electrostatic force on a pair of point charges with the equal magnitude and the same sign on the axis is attractive under proper conditions．