We propose a proof-of-principle experiment to test a new scheme to produce a single-cycle radiation pulse in free-electron lasers (FELs). Here, a few ${\it\alpha}$-BBO crystals will be first used to produce an equally spaced laser pulse train. Then, the laser pulse train illuminates the cathode to produce a frequency-chirped electron bunch train in a photocathode rf gun. Finally, the frequency-chirped electron bunch train passes through a tapered undulator to produce a quasi-single-cycle THz pulse. This experiment should allow comparison and confirmation of predictive models and scaling laws, and the preliminary experimental results will also be discussed.