Effects of hydrogen doping on the internal friction (IF) of ternary Ti50Ni50-xCux (x=15, 20, 25) shape memory alloys, prepared by rolling and annealing laminating Ti and Ni-Cu alloy sheets, have been measured with a damping mechanical analyzer in a forced bending oscillation mode at temperatures from 173K to 423K at three frequencies, 0.1, 1 and 5Hz. The effects of hydrogen doping on IF are common to the three alloys: a hydrogen IF peak appears at around 260K; the IF peak value (tanφ) increases rapidly with increasing hydrogen concentration up to tanφ=0.03 at 0.5at% and then decreases; the peak temperature also increases rapidly and then gradually decreases. From the frequency dependence of the peak temperature, the activation energy E and the pre-exponential factor ω0 have been analyzed to be E=0.6-0.7eV and ω0=1013-14s-1. The origin of the hydrogen IF is interpreted to be the Snoek-Koester effect due to interaction of twin boundary dislocations and segregated hydrogen atoms. Effects of hydrogen on mechanical properties of the alloys have also been studied.