The Levenberg-Marquardt method is a famous numerical method for solving system of nonlinear equations and nonlinear least-squares problems. By using trust region technology, the Levenberg-Marquardt method with a new choice of the LM parameter is presented in this paper. The new choice of the LM parameter can be considered as a generalization of some other choices. By using the H\"olderian local error bound of function and H\"olderian continuity of its Jacobian instead of the commonly used local error bound and Lipschitz continuity of Jacobian respectively, the sequence generated by the Levenberg-Marquardt method has been shown to have global convergence, and to converge to a solution of nonlinear equations superlinearly and even quadratically for some special parameters. Numerical results show that the method performs well for singular problems.