In this paper, an investigation on broadband IR supercontinuum generation in single crystal sapphire fibers is presented. It is experimentally demonstrated that broadband IR supercontinuum spectrum (up to 3.2microm) can be achieved by launching ultra-short femtosecond laser pulses into single crystal sapphire fiber with a dimension 115microm in diameter and 5cm in length, which covers both the near IR spectral region and the lower end of the mid-IR spectral range. Furthermore, the mechanism of supercontinuum generation in single crystal sapphire fibers is briefly addressed. When the fiber length is shorter than the dispersion length, the self-phase modulation dominates the broadening effect. In this case, the broad supercontinuum spectrum with a smooth profile can be obtained. However, when the fiber length is longer than the dispersion length, the soliton-related dynamics accompanied by the self-phase modulation dominates the broadening effect. There are discrete spikes in the spectrum (corresponding to different order solitons). The above assumption of supercontinuum generation mechanism is quantitatively modeled by the computer simulation program and verified by the experimental results. Thus, one can adjust the spectral profile by properly choosing the length of the sapphire fibers. The broad IR spectral nature of this supercontinuum source can be very useful in a variety of applications such as broadband LADAR, remote sensing, and multi-spectrum free space communications.