The maximum velocity of a mobile vortex experiences during its movement is generally limited by the phenomenon of flux-flow instability (FFI), which necessitates weak vortex pinning and fast heat removal from non-equilibrium electrons. We here demonstrate exfoliations and nano-fabrications of Bi$_{2}$Sr$_{2}$Ca$_{2}$Cu$_{3}$O$_{10+\delta}$ crystalline nanostrips, which possess a rather weak pinning volume of vortices, relatively low resistivity, and large normal electron diffusion coefficient. The deduced vortex velocity in Bi$_{2}$Sr$_{2}$Ca$_{2}$Cu$_{3}$O$_{10+\delta}$ crystalline nanostrips can be up to 300 km/s near the superconducting transition temperature, well above the speed of sound. The observed vortex velocity is an order of magnitude faster than that of conventional superconducting systems, representing a perfect platform for exploration of ultra-fast vortex matter and a good candidate for fabrications of superconducting nanowire single photon detectors or superconducting THz modulator.