Abstract: The Complex Geodesic Problem(CGP) is firstly named and it has been defined scientifically in this paper.There are 10 types of CGP.All of them have been listed with the known data and the found data.The practical models have been shown by the nested method too.The unique correct solution will be obtained for any distance between two points and any type of CGP,because the accurate positions of the critical point and the equater crossing of a geodesic are used as a determinate condition.The models are suitable well to electronic computers.The programs all are terse and the machine time is shorter.It will take just about one minute to solve any one problem of them.There is no limit on distance between the two points from one to twenty thousand kilometers and the expect accuracy can be obtained as well as the nested method.