Quasi-one-dimensional SnSe nanoribbons (NRs) show a wide range of applications in optoelectronics fields such as optical switches, photodetectors, and photovoltaic devices due to the suitable band gap, strong light-matter interaction, and high carrier mobility. However, it is still challenging to grow high-quality SnSe NRs for high-performance photodetectors so far. In this work, we successfully synthesized high-quality p-type SnSe NRs by chemical vapor deposition and then fabricated near-infrared photodetectors. The SnSe NR photodetectors show a high responsivity of 376.71 A W−1, external quantum efficiency of 5.65 × 104 %, and detectivity of 8.66 × 1011 Jones. In addition, the devices show a fast response time with rise and fall time of up to 43 μs and 57 μs, respectively. Furthermore, the spatially resolved scanning photocurrent mapping shows very strong photocurrent at the metal-semiconductor contact regions, as well as fast generation-recombination photocurrent signals. This work demonstrated that p-type SnSe NRs are promising material candidates for broad-spectrum and fast-response optoelectronic devices.