In recent years, high-speed signal reconstruction with sub-Nyquist sampling have attracted the attention of researchers in the signal processing field. Nonetheless, such methods have been limited either by the need to utilize multiple cameras, or relying on newly designed imaging hardware. In this paper, we propose a high-speed periodic motion reconstruction method, obtained by randomly delaying the camera exposure. This allows it to utilize a conventional off-the-shelf camera. In addition, the proposed method compensates the rolling shutter effect, which is inevitable if the camera’s image sensor is made of complementary metal-oxide semiconductor (CMOS), while reconstructing the high-speed periodic motion. Exhaustive and comparative experiments have been conducted to validate the proposed method, which showed promising performance in terms of reconstruction error, and effective compensation of the rolling shutter effect.