The origin of photogenerated terahertz radiation pulse emitted from current-biased superconducting YBa 2 Cu 3 O 7Ϫ␦ thin films excited by femtosecond optical laser pulses is delineated. By investigating the performance of the transient terahertz radiation generated under different operating parameters, pulse reshaping in the measured terahertz electric field caused by the kinetic inductance of the superconducting charge carriers is identified. After recovering the original wave forms of the emitted terahertz pulses, the transient supercurrent density directly correlated to the optically excited quasiparticle dynamics is obtained. A fast decreasing component of about 1.0 ps and a slower recovery process with a value of 2.5 ps are unambiguously delineated in the optically induced supercurrent modulation. The radiation mechanism of the transient terahertz pulse related to nonequilibrium superconductivity is discussed.