Stress amplitude dependence of internal friction (tanδ) of a Ti-base shape memory alloy, Ti-24mol%Nb-3mol%Al, with a well developed texture is investigated by a dynamic mechanical analyzer (DMA) in a tensile mode. In the martensite (C-orthorhombic) phase, tan was 0.01~0.05 and was much higher than that of the parent phase in all the test conditions. This means that the martensite/martensite interfaces move under the external sinusoidal stress. In addition to this high background, tanδ-peak appeared at around 153K. The tanδ-peak height clearly depended also on the stress amplitude (10~50MPa). In addition, a threshold stress for the appearance of the tanδ-peak existed in the DMA test and it was in good agreement with the yield stress (0.2% proof stress) in a tensile test at 153K. These results mean that a long-range motion of twin-boundaries is necessary for the appearance of the tanδ-peak.