Wire conical monopole antennas at an arbitrarily conducting ground plane are analyzed by the Method of Moment (MM).The basis function presented by RWG is used to present the current on the surfaces.The triangular basis function is used to present the current on the wires,and a special basis function is used to present the current on the wire/surface junctions.Finally,as an example,conical antennas on a circular and a square ground plane in 400MHz~2100MHz frequency band are analyzed respectively.Numerical results and comparisons show the efficiency of the method and the finite ground plane plays an important role in adjusting the impedance matching.