This paper focuses mainly on developing single-step explicit integration algorithms considering the implicit treatment of velocity. A novel explicit algorithm (GSSI) is proposed and recommended as a self-starting dissipative alternative to the central difference methods in transient analysis. GSSI not only shares the same advantages as the central difference methods, such as second-order accuracy and computational cost, but also achieves flexible dissipation control and self-starting property. Remarkably, GSSI provides a significantly larger stability bound than the central difference methods in the damped case. GSSI imposes two algorithmic parameters ( and ) to flexibly adjust numerical dissipation at the bifurcation point. In general, the controls numerical dissipation at the bifurcation point, while the further adjusts the amount of dissipation in the low-frequency range. Spectral analysis and numerical examples are given solved to show the superiority of GSSI over the existing single-step explicit methods with respect to accuracy, stability, and dissipation control.