Abstract: A meshless time-domain method for a solution of the Maxwell’s equations is developed. Clouds of points are distributed all over the computational domain, which is realized by a technique newly developed for distributing points directly and quickly. The spatial derivatives are approximated by using a local leastsquare curve fit in each cloud of points,and a particular approximate Riemann solver is constructed for computing the physical flux of the governing equations. Then an explicit four-stage Runge-Kutta scheme is used to advance the Maxwell’s equations in time. The numerical radar cross sections of typical 2D objects are obtained by using the present method and are in good agreement with those of other methods in open literatures. The paper ends with the computation of scatttered fields of complicated aerodynamic bodies like aircraft models, which show the present method has the ability to accommodate complex geometries with multi-element or multi-component.