Droplet manipulation is the cornerstone of many modern technologies. It is still challenging to drive the droplet motion on nonslippery surfaces flexibly. We present a droplet manipulation method on nonslippery polymer surfaces based on the corona discharge. With the corona discharge of two-needle electrodes with opposite polarities, the droplet's charge polarity can be switched, which results in the directionally droplet transport on a charged polymer surface with the oscillation. Here, such droplet behaviors are presented in detail. Dependence of the motion on the critical distance and driving distance between the droplet and the needle electrode is revealed. The driving mechanism is verified by experiments and simulations. This work enriches the droplet manipulation techniques on nonslippery surfaces for various applications, such as combinatory chemistry, biochemical, and medical detection.