The hydrogen internal friction peak (HIFP) in amorphous (a-) Zr60Cu40−yAly (y=0,10), a-Zr50Cu50, a-Zr40Cu60 and a-Zr40Cu50−xAl10Six (x=0,1,3) are studied to pursue a high-strength and high-damping performance as well as the underlying process for the HIFP in a-alloys. The tensile strength, σf, of a-Zr60Cu30Al10, a-Zr40Cu50Al10 and a-Zr40Cu49Al10Si1 increases from about 1.5 GPa to 2 GPa with increasing hydrogen concentration, CH, to 20 at%. One part of a-Zr60Cu30Al10, a-Zr40Cu50Al10 and a-Zr40Cu49Al10Si1 specimens show a very high HIFP beyond 3×10−2 in the as hydrogen charged state, where the hydrogen induced structural relaxation (HISR) proceeds above room temperature. A maximum value of the HIFP, Qp−1, after the HISR shows a moderate increase with increasing CH, about 1×10−2 at CH of 10 at%. The combination of σf and Qp−1 data indicates that a-Zr60Cu40Al10(H), a-Zr40Cu50Al10(H) and a-Zr40Cu49Al10Si1(H) after the HISR are potential materials with a high-strength and high-damping performance. The peak temperature of the HIFP, Tp, at 10 at%H is 309 K, 270 K and 220 K with the measurement frequency of about 200 Hz for a-Zr40Cu49Al10Si1, a-Zr40Cu50Al10 and a-Zr60Cu30Al10, respectively. It is noted that Tp found for a-Zr40Cu49Al10Si1 shows a breakthrough for an elevation of Tp of the HIFP in a-alloys, and that a composite material composed of these a-alloys can serve a high-damping performance in a wide temperature range or a wide frequency range. For the underlying process of the HIFP, the Qp−1 vs. CH data shows a camel’s humps like change for a-Zr50Cu50 and a-Zr40Cu60, suggesting that only one part of hydrogen atoms can contribute to the HIFP . In contrast, Qp−1 shows a monotonous increase with increasing CH for CH below 20 at% for a-Zr60Cu40−yAly (y=0,10) and a-Zr40Cu50−xAl10Six (x=0,1,3), suggesting that most of hydrogen atoms are associated with the HIFP in the a-alloys. For the relaxation parameters of the HIFP, values of 1/τ0 fall in the range expected for a simple relaxation process for a-Zr60Cu40−yAly (y=0,10) and a-Zr40Cu50−xAl10Six (x=0,1,3), but are extremely high for a-Zr50Cu50 and a-Zr40Cu60, where τ0 denotes the pre-exponential factor of the relaxation time. These results are discussed in the light of the amorphous structures in the a-alloys.