To optimize the performance of a heat engine in a finite-time cycle, it is important to understand the finite-time effect of thermodynamic processes. Previously, we have shown that extra work is needed to complete a quantum adiabatic process in finite time, and proved that the extra work follows a C/τ^{2} scaling for long control time τ. There the oscillating part of the extra work is neglected due to the complex energy-level structure of the particular quantum system. However, such oscillation of the extra work cannot be neglected in some quantum systems with simple energy-level structure, e.g., the two-level system or the quantum harmonic oscillator. In this paper, we build the finite-time quantum Otto engine on these simple systems, and find that the oscillating extra work leads to a jagged edge in the constraint relation between the output power and the efficiency. By optimizing the control time of the adiabatic processes, the oscillation in the extra work is utilized to enhance the maximum power and the efficiency. We further design special control schemes with the zero extra work at the specific control time. Compared to the linear control scheme, these special control schemes of the finite-time adiabatic process improve the maximum power and the efficiency of the finite-time Otto engine.