Abstract: Based on Benthien_Gurtin's principle of minimum transformed energy in linear elastodynamics in Laplace space, functional in the form of single convolution integral is obtained by restoring the functional in the Laplace space back into the original space. By successively spatial and temporal discretization, functionals after spatial and temporal discretization are obtained respectively. Cubic Hermite interpolation functions with a non-time-step parameter are adopted to approximate the nodal displacement in local time domain. A unconditionally stable step-by-step integration method is finally presented based on the variational operation. The parameter can control the stability of the algorithm better and its optimum value is selected according to the unconditionally stable analysis. Examples show that the algorithm possesses satisfactory accuracy and it is an effective method for the investigations of dynamic response problems in practical engineering.