In this study, a refractive-index guiding single-crystal fiber (SCF) with air–solid cladding was proposed and numerical simulation investigation was carried out. In general, refractive-index guided cladding was constructed through air-holes in the solid material. It resulted in the effective reduction in the number of guided-modes, and the single-mode and few-mode transmission could be realized. The influences of different materials with different refractive indices, cladding structure, and fabrication errors on the confinement loss and effective guided-mode number with the variation in wavelength from 2.5 to 3.2 µm were numerically investigated by the finite element method. Thus, the optimal design of the SCF was successfully obtained. This study may open a new avenue for the design of SCFs and their applications in the fiber lasers and sensors.