We propose and demonstrate wavelength conversion of spectrum-sliced broadband amplified spontaneous emission light sources based on hybrid four-wave mixing (HFWM) in highly nonlinear, dispersion- shifted fibers (HNL-DSFs). The theory of HFWM between coherent pumps and incoherent signal is analyzed. The degenerate HFWM is demonstrated experimentally in a 1-km-long HNL-DSF, where the coherent pump light is provided by a tunable cw laser source and the incoherent signal light is spectrum-sliced from a broadband amplified spontaneous emission light source. A conversion efficiency of about -20.4 dB and a bandwidth of about 38 nm are measured. The experimental result agrees well with the theoretical analysis.