Femtosecond laser excited terahertz waves have been widely used in various fields. Herein, we demonstrate a novel method to generate terahertz radiation from a terahertz electro-optic crystal excited by infrared supercontinuum radiation (wavelengths > 1 μm), which is produced via the interaction between a femtosecond laser and a transparent solid medium. This approach yields single-cycle, low-frequency, broadband terahertz radiation. In the femtosecond laser-induced ionization process in a medium, both infrared supercontinuum radiation and terahertz radiation are simultaneously generated. When the resulting infrared supercontinuum radiation and terahertz radiation concurrently enter into an electro-optic crystal, the presence of the infrared supercontinuum radiation may interfere with the detection of the intrinsic terahertz radiation. By filtering the infrared supercontinuum radiation with narrowband filters, a new strategy is proposed for investigating the response of the electro-optic crystal in infrared spectral region.