Abstract: In this paper, a time-domain identification method based on the complex modal analysis technique is presented for the multi-degree -of-freedom structural systems with visco and hysterestic dampings, in which the identifying problem is converted into an unconstraint optimization procedure with a set of new variables (systematical parameters) by means of a tranformation that the Hessian matrix is created with the sensitivity matrix of the structural system. The approach has the advantages of concise algorithm, rapid convergence rate, high estimate accuracy, and realization of auto-selection of model order, etc. A numerical example is presented to illustrate the effectiyeness of this method. The present paper is the first of two companion papers. The nonlinear identification of the same problem is given in the second paper.