As a sort of quasi-brittle materials, fracture toughness of bulk metallic glasses (BMGs) is of paramount importance for their engineering application. Among the BMG families, Cu-based BMGs are of interest due to their low cost, high strength and less brittleness. As indicated in previous work, the Cu₄₉Hf₄₂Al₉ BMG exhibits a good combination of toughness and glass forming ability (GFA). Moreover, toughness of BMG significantly depends on alloy composition. In the Zr-Cu-Al system, it was suggested that increasing the Al content in the alloy does not favor to the plasticity of the glass. Then, it is expected that Al-free Cu-Hf-Ti BMGs may be tougher than the Cu₄₉Hf₄₂Al₉ BMG. In addition, notched cylindrical samples were used for the toughness assessment in previous investigation, which probably introduce an overestimation in toughness in comparison with archival data of engineering materials. To obtain the glassy plate samples for toughness measurements to meet the ASTM E399 requirement, alloys with robust GFA is necessary. In this work, the composition dependence of GFA for ternary Cu-Hf-Ti alloys was revisited. The alloys with the optimal GFA are located around the Cu₅₆Hf₂₇Ti₁₇ and Cu₅₇Hf₂₇Ti₁₆. The critical diameter to form the BMG rods was determined to be 5 mm. Then, the Cu₅₆Hf₂₇Ti₁₇ BMG plates of 2.5 mm in thickness can be fabricated as the specimens for toughness assessments. Using the single-edge notched specimen for three-point bending test, the notch toughness K _Q of Cu₅₆Hf₂₇Ti₁₇ BMG was determined to be(92±10) MPa·m^1/2. It is nearly doubled with respect to the Cu₄₉Hf₄₂Al₉ BMG (K_Q=(56±9) MPa·m^1/2).It means that the Cu₅₆Hf₂₇Ti₁₇ BMG is the toughest among currently-available Cu-based BMGs. Such high toughness of Cu₅₆Hf₂₇Ti₁₇ BMG also correlates with its moderate Poisson's ratio (ν=0.361) and low shear modulus (G=38.6 GPa). The enhanced toughness of Cu₅₆Hf₂₇Ti₁₇ BMG is associated with the extended plastic zone size at the notch tip with the proliferation of shear banding events. The fact that the Cu₅₆Hf₂₇Ti₁₇ superior to Cu₄₉Hf₄₂Al₉ BMG in toughness seemingly supports that Al element has an unfavorable effect on the toughness of Cu-Zr/Hf-based BMGs.