High-strength Cu-based bulk glassy alloys with a large supercooled liquid region in Cu-TM-Al (TM=Zr, Hf) ternary and quaternary systems were synthesized by copper mold casting. The maximum diameter was 3.0 mm for the Cu₅₀Zr₄₅Al₅, Cu_52.5Hf₄₀Al_7.5, Cu₅₀Hf_42.5Al_7.5 and Cu₅₀Hf_22.5Zr_22.5Al₅ alloys. The glass transition temperature (T_g), temperature interval of supercooled liquid region ΔT_x(=T_x — T_g) and reduced glass transition temperature (T_g/T_l) are in the range from 701—781 K, 54—91 K and 0.61—0.63, respectively. The Cu-based bulk glassy alloys exhibit good mechanical properties, i.e., 102—128 GPa for Young's modulus, 1885—2370 MPa for compressive fracture strength, up to about 0.6% for compressive plastic elongation, and 550—670 for Vickers hardness. The finding of the new Cu-based bulk glassy alloys with large supercooled liquid region above 54 K, high reduced glass transition temperature above 0.60, and high fracture strength above 1885 MPa is encouraging for future development as a new type of bulk alloys which can be used as structural materials.