High-strength Cu-based bulk glassy alloys were formed in the Cu–Hf–Ti system by the copper mold casting and melt clamp forging methods. The maximum diameter is 4 mm for the Cu60Hf25Ti15 alloy. The substitution of Hf in the Cu60Hf40 alloy by Ti causes an increase in the glass-forming ability (GFA). As the Ti content increases, the glass transition temperature (Tg) decreases, while the crystallization temperature (Tx) shows a maximum at 5% Ti and then decreases, resulting in a maximum supercooled liquid region ΔTx (= Tx − Tg) of 78 K at 5% Ti. The liquidus temperature (T1) has a minimum of 1172 K around 20% Ti, and hence, a maximum Tg//T1 of 0.62 is obtained at 20% Ti. The high GFA was obtained at the compositions with high Tg/T1. The bulk glassy alloy exhibits tensile fracture strength of 2130 MPa, compressive fracture strength of 2160 MPa, and compressive plastic elongation of 0.8 to 1.6%. The new Cu-based bulk glassy alloys with high Tg/T1 above 0.60, high fracture strength above 2100 MPa, and distinct plastic elongation are encouraging for future development as a new type of bulk glassy alloy that can be used for structural materials.