Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate 5.47×10^{8} quantum-proof random bits while consuming 4.39×10^{8} bits of entropy, expanding our store of randomness by 1.08×10^{8} bits at a latency of about 13.1 h, with a total soundness error 4.6×10^{-10}. Device-independent quantum randomness expansion not only enriches our understanding of randomness but also sets a solid base to bring quantum-certifiable random bits into realistic applications.