Perovskite materials have attracted extensive attention in photodetection owing to their excellent light absorption capability and high carrier generation efficiency. Among them, the lead-free perovskite Cs₃Bi₂I₉ has been widely studied due to its low toxicity and outstanding X-ray sensitivity. However, its relatively low carrier mobility severely restricts the effective transport of photogenerated carriers, thereby limiting key device performance metrics such as responsivity, external quantum efficiency, and detectivity. To address this challenge, a Cs₃Bi₂I₉/carbon nanotubes (CNTs) composite photodetector is developed by introducing CNTs networks as efficient charge transport pathways into the Cs₃Bi₂I₉ photosensitive layer. This hybrid architecture enables a decoupled design of light absorption and carrier transport, where Cs₃Bi₂I₉ serves as the primary light-harvesting medium while CNTs facilitate rapid carrier extraction and transport, effectively suppressing carrier recombination. As a result, the device exhibits excellent performance under 405 nm illumination, achieving a responsivity of 1.44 × 10⁵ A/W and a detectivity of 1.15 × 10¹⁶ Jones. In addition, a high X-ray sensitivity of 2.088 × 10⁴ μC/(Gy_air·cm²) is achieved. These results demonstrate a new route for advancing lead-free high-performance broadband perovskite optoelectronic devices.