Martensitic transformation (MT) and the internal friction (IF) behavior of the initially amorphous Ti-rich Ti-Ni-Cu melt-spun ribbon annealed at 400°C for 10 h were investigated by using DSC and dynamic mechanical analysis (DMA). The annealed ribbon shows B2 structure with strong preferential (110) orientation and exhibits B2↔B19 MT with the temperature hysteresis of 13°C. DMA tests show that the internal friction is frequencies dependence at 1-50 Hz. The tanδ values decrease with the increasing frequency, but it does not meet the 1/f dependence. Isothermal DMA tests show that the tanδ value at a temperature of 15°C in the MT zone increases quickly from 0.005 to 0.045 with the increasing isothermal intervals and keep stable subsequently. The isothermal time to complete the MT can be determined by the DMA tanδ curve directly.