We demonstrate multiple-channel wavelength conversions of second harmonic and sum frequency generations in a silicon carbide photonic crystal cavity. The cavity is designed to have multiple modes including a nanocavity mode and Fabry-Pérot modes. Multiple-channel wavelength conversions in the nanocavity and Fabry-Pérot modes are shown experimentally. Furthermore, we investigate the polarization characteristics of wavelength-converted light. The experimental results of the polarization are in good agreement with calculation.