The transient optical signal with wide bandwidth widely exists in laser interference velocity measurement, optical communication and some other fields. It has wide bandwidth and non-repeatability. The existing direct or indirect optical pulse measurement technologies cannot be applied to the measurement of such signal. We use time-wavelength mapping chirped optical pulse to sample the transient optical signal at a high rate under the four wavelength mixing effect, and magnify the signal time scale by using time-stretching technology and dispersive medium. The bandwidth and sampling rate of the back-end electrical record system are increased by times. The experimental results show that the measurement of light beat-frequency signal with bandwidth of 56.978 GHz in real-time is feasible and the equivalent measurement time resolution is 3.7 ps, which verifies the validity of the proposed method.