A new type of superconductive true random number generator (TRNG) based on a negative-inductance superconducting quantum interference device (nSQUID) is proposed.The entropy haessed to generate random numbers comes from the phenomenon of symmetry breaking in the nSQUID.The experimental circuit is fabricated by the Nb-based lift-off process.Low-temperature tests of the circuit verify the basic function of the proposed TRNG.The frequency characteristics of the TRNG have been analyzed by simulation.The generation rate of random numbers is expected to achieve hundreds of megahertz to tens of gigahertz.