Lead halide hybrid perovskites have been intensively explored as light‐harvesting materials owing to their unique optoelectrical characteristics and simple deposition method. However, the toxicity and instability problems are still hindering their further development and applications. Herein, stable lead‐free double perovskite Cs2AgBiBr6 single crystals (SCs) with outstanding photoelectric properties are prepared. When symmetric Au electrodes are used, the resulting photodetectors (PDs) can have broad spectral response, high responsivity of 4.88 A W−1, external quantum efficiency of 1100%, and detectivity of 1.22 × 1013 Jones, respectively. More interestingly, when asymmetric electrodes (Au and Ag) are used, the authors obtain the first reported self‐driven PD based on the lead‐free perovskite SC, to the best of the authors’ knowledge. The device exhibits good photoresponse properties at a bias of 0 V. Both devices hold short response time at µs scale, which are among the best reported lead‐free perovskite PDs. Both devices demonstrate decent stabilities in air without encapsulation. All results demonstrate that Cs2AgBiBr6 SCs have great potential in the application of optoelectronic devices.