In this paper, newly designed plastic Cu51Zr37Ti8Ni4 bulk metallic glass has been successfully fabricated. By purposely increasing the liquidus temperature in a quaternary Cu–Zr–Ti–Ni alloy system, glass-forming ability of as-cast bulk metallic glasses shows a desired decrease trend. As-cast Cu51Zr37Ti8Ni4, which has a lower glass-forming ability and a higher liquidus temperature than Cu52Zr37Ti8Ni3, is of monolithic amorphous structure, and also displays remarkable plasticity of 10.5% together with the fracture strength of 2145MPa. Multiple and interactive shear bands can be discovered on the fracture surface of fractured Cu51Zr37Ti8Ni4. In addition, the deformation of Cu51Zr37Ti8Ni4 shows serrated flow behavior. By a statistics analysis of serrations in the stress–time curve, the serrated flow behavior of the sample follows the self-organized critical behavior. This work suggests that, with the aid of CALPHAD, composition design of plastic bulk metallic glasses can be achieved according to the liquidus perspective.