Quantum mechanics provides the means of generating genuine randomness that is impossible with deterministic classical processes. Remarkably, the unpredictability of randomness can be certified in a manner that is independent of implementation devices. Here, we present an experimental study of device-independent quantum random number generation based on a detection-loophole-free Bell test with entangled photons. In the randomness analysis, without the independent identical distribution assumption, we consider the worst case scenario that the adversary launches the most powerful attacks against the quantum adversary. After considering statistical fluctuations and applying an 80 Gb x 45.6 Mb Toeplitz matrix hashing, we achieve a final random bit rate of 114 bits/s, with a failure probability less than 10(-5). This marks a critical step towards realistic applications in cryptography and fundamental physics tests.