The distance-minimizing data-driven method introduces a new computing paradigm and focuses on computational solid mechanics research. This method enables direct input of discrete material data sets (stress-strain pairs), bypassing the empirical constitutive modeling process and reducing modeling errors and uncertainties. To apply this method to boundary value problems, it is necessary to define a distance functional from the solution set to the material data set, seeking the functional extremum that satisfies the strain-displacement relationship and equilibrium equation from the material data set. In this study, we extend the method to structural dynamics, using the structural dynamic equilibrium equation as a constraint for the distance functional. We derive data-driven computing formulas, analyze the value of the constant matrix in the formula, and develop an algorithm for solving structural dynamic responses. The accuracy and efficiency of the proposed method are validated through linear and nonlinear dynamic response analyses of single-degree-of-freedom systems and multi-degree-of-freedom truss structures. Within this theory, the final value from the previous moment serves as the initial value for the current moment, facilitating faster numerical solutions and reducing computational time. Additionally, the material data set accommodates both linear and nonlinear material behaviors. It is also found that when the amount of material data exceeds 100, the amount of material data and excitation step minimally impact computational accuracy, with the signal-noise ratio (SNR) becoming the primary factor. Under the same conditions, the amount of material data and excitation step significantly affect computational efficiency, while the influence of SNR can be ignored. This study provides theoretical support for the development of data-driven dynamic solvers.