This paper presents the method of complex ray direction determination

withwhich the trace of complex ray direction can be determined. And this method analyzes the scattering fields in space which are produced by the target for complex source beam in frequent domainand complex source pulsed beam in time domain. There is the same accuracy between this methodand the complex ray tracing method. Furthermore this method can reduce the unknown four-dimensional（4-D）variables of the latter to 2-D ones

and 2-D variables to l-D one. And this effecientmethod solves the problems that we face when using the complex ray poroxial approximationmethod. This paper also analyzes and calculates the scattering fields in space of conduct plate

conduct sphere and concave conduct half sphere shell for the 3-D vector complex source beam. The numerical results of this method completely agree with those of complex ray tracing method.