In this paper, the frequency-dependent noise figure of a continuous photonic time-stretch system is theoretically analyzed and experimentally demonstrated. Mathematic analysis discloses that the frequency-dependent noise figure in the continuous photonic time-stretch system is mainly owing to the dispersion-induced phase shift in the link. In the experiment, a completely continuous signal is reconstructed with time-interleaved joining of four sections of time-stretched signals from optical wavelength-division de-multiplexing channels. The result of the frequency-dependent noise figure property agrees well with that of theoretical analysis.