In this study, a novel composite time integration method is proposed for more accurately and efficiently solving typical structural dynamic problems. In this method, the second-order accuracy is ensured for dynamic problems. First, the stability, accuracy properties, local truncation error, and global error are analyzed and compared with available state-of-the-art methods in the literature. Then, three sets of parameters are recommended and discussed, and optimization of these parameters results in a high accuracy and efficiency of the proposed method. Finally, three classical examples with high-frequency vibrations, where a large ratio of the time step size to the period is adopted, are presented to demonstrate the accuracy, efficiency, and applicability of the proposed method.