In the present article, a new surrogate-assisted evolutionary algorithm for dynamic identification problems with unknown parameters is presented. It is based on the combination of the response surface (RS) approach (the surrogate model) with differential evolution algorithm for global search. Differential evolution (DE) is an evolutionary algorithm where N different vectors collecting the parameters of the system are chosen randomly or by adding weighted differences between vectors obtained from two populations. In the proposed algorithm (called DE-Q), the RS is introduced in the mutation operation. The new parameter vector is defined as the one minimizing the second-order polynomial function (RS), approximating the objective function. The performances in terms of speed rate are improved by introducing the second-order approximation; nevertheless, robustness of DE algorithm for global minimum search of objective function is preserved, because multiple search points are used simultaneously. Numerical examples are presented, concerning: search of the global minimum of analytical benchmark functions; parameter identification of a damaged beam; parameter identification of mechanical properties (masses and member stiffnesses) of a truss-girder steel bridge starting from frequencies and eigenvectors obtained from an experimental field test