We report the design and testing of a novel linear scanning periodic optical delay line (ODL) by use of a helicoid reflective mirror based on a tilted parabolic generatrix that was driven by an electrical motor for a periodic change in the optical path length of the reflected light beam. The divergence and pulse front distortion of the optical beam reflected by the helicoid reflective mirror were simulated based on differential geometry. With a round-trip pass arrangement, a scanning range of delay time as large as $100\mathrm{ps}$ was obtained by spinning the helicoid reflective mirror with a pitch distance of $7.5\mathrm{mm}$ . This periodic ODL was used in an optical second-harmonic generation autocorrelator to test the linearity and temporal resolution in comparison with the autocorrelation signal obtained using an ODL structured with a motorized linear translation stage. Experiments demonstrate that our helicoid optical delay device may provide exceptional performance for optical interference, high-resolution terahertz time-domain spectroscopy, and general optical pump–probe experiments.