Two algorithms are proposed for direct time integration of an equation of motion of structural dynamics problems. The performance of the proposed methods is examined by evaluating stability, order of accuracy, numerical dissipation, and algorithmic damping. The results show that critical time for instability of the proposed algorithms is larger than those of conditionally stable methods. The numerical dissipation is shown to be explicitly less than other methods. Furthermore, the proposed algorithms are non-dissipative in the low-frequency range and have favorable damping in mid-and high-frequency regimes. Three examples are carried out to evaluate the feasibility and effectiveness of the proposed algorithms.