Abstract: Taking the first-order equations of motion as the model problem, a novel condensed test function is constructed by using its non-self-adjoint property and then a new type of high-performance Galerkin finite element, called condensed element, is proposed. The proposed element, being of one-step type and unconditionally stable, can produce O(h^2\bar m + 2) super-convergence for displacement and velocity at end-nodes of elements of degree \bar m , which is two orders higher than traditional elements. Further, an efficient adaptive time step-size algorithm is achieved without additional nodal displacement recovery technique being used. The paper gives a brief report of this initial and promising study with some preliminary numerical examples given to show the feasibility and effectiveness of the proposed approach.