Based on density functional theory, we perform first-principles investigations to study the optical properties of the O-, F- and H-terminated SiC nanoribbons with armchair edges (ASiCNRs). By irradiating with an external electromagnetic field, we calculate the dielectric function, reflection spectra, energy loss coefficient and the real part of the conductance. It is demonstrated that the optical constants are sensitive to the low-energy range, different terminal atoms do not make much difference in the shape of the curves of the optical constants for the same-width ASiCNR, and the optical constants of wider nanoribbons usually have higher peaks than that of the narrower ones in low energy range. We hope that our study helps in experimental technology of fabricating high-quality SiC-based nanoscale photoelectric device.