In this paper we propose a new method of nonlinear transformation(Eigen-Mapping) to treat the eigenvalue problems in quantum mechanics as examples.The basic idea is to make the matrix of some operator we concerned diagonalization through introduction of small undetermined parameters and establishment equations for matrix elements.These problems can be devided into two types based on that there are or not 1st order approximate solution for them(in sense of the perturbation theory).In either type we consider also two cases of degenerate and nondegenerate.To obtain solution or approximate solution for eigenvalue problems,it is given the procedures of the method and usable formulas exhaustively.Seven examples in this paper are a common sight in general course of quantum mechanics.The results from them are compared with that from other approximate methods(for examples: perturbation method and variation method).After checking the results obtained,we can see that this new method has many advantages.