Metallic glasses (MGs) with a long-range disordered structure and without crystallographic defects have attracted great research attention. Owing to the disordered structure, MGs usually exhibit excellent physical and chemical properties, comprehensive mechanical performances, and high thermal stability. Minor doping of elements can effectively enhance the glass-forming ability of MGs and then seriously affect the yielding strength and plasticity. In this study, a family of Cu₄₅Zr₄₅Al_10-xAg_x (x = 1, 2, 3, and 5, atomic fraction, %) MG with minor Ag-addition was prepared by suction casting. A nanoindentation test was used to investigate the influence of Ag content on the nanoplastic deformation behavior of the Cu-Zr-Al-based MG. In terms of the empirical equation, the strain rate sensitivity index (m) was acquired to calculate the shear transformation zone volume during the nanoindentation creep process. Based on the Kohlrausch-Williams-Watts equation, the relaxation evolution was obtained. As Ag content approaches 5%, m attains its minimum, indicating that the creep resistance of the Cu-Zr-Al-based MG is the largest. The creep behavior of the system depends on the loading rate, i.e., the faster the loading rate, the lower the creep resistance. With an increase in the Ag content, the exponent stretch is increased, and the hardness of the Cu-Zr-Al-based MG was enhanced combined with an increased plasticity. This study presents the fundamental information of the relationship between the thermal dynamic and mechanical properties of the Cu-Zr-Al-based MG.