Quasi-two-dimensional organic–inorganic hybrid halide perovskite materials have attracted extensive attention in the field of optoelectronic devices owing to their unique photoelectric properties. However, lead toxicity greatly hinders their practical applications. Using environmentally friendly elements to substitute lead is an effective solution, but even worse stability and photoelectric performance pose a great challenge for further device fabrication. Here, high-performance lead-free photodetectors (PDs) are developed based on a BA2FAn-1SnnI3n+1 (n = 1, 2) film via a one-step spin coating method. The films could be stable for two to three hours in ambient conditions. The devices show the dark current of 2.1 × 10−9 (n = 1) and 2.6 × 10−9 A (n = 2), the on/off ratio of 458 (n = 1) and 1108 (n = 2), and the detectivity of 1.46 × 1013 (n = 1) and 6.23 × 1012 Jones (n = 2), which were outstanding in the reported Sn-based PDs. The excellent performance is attributed to the low Sn4+ self-doping realized by adding Sn powder and SnF2 in a precursor solution in the synthesis process and the high-performance optoelectronic properties of FA-based perovskite. This study demonstrates that BA2FAn-1SnnI3n+1 is a promising material for photovoltaic devices.