Black phosphorus (BP) is a promising material for ultrafast and broadband photodetection because of its narrow bandgap from 0.35 eV (bulk) to 1.8 eV (monolayer) and high carrier mobility. Although photodetectors based on BP with different configurations have been reported, high photosensitivity was mostly observed in the visible range. A highly efficient BP-based infrared photodetector operated in the telecom spectral range, especially at 1550 nm, has not been demonstrated. Here, we report a Schottky-type photodetector based on thin BP flakes, operating in a broad spectral range from visible (635 nm) to infrared (1550 nm). A responsivity as high as 230 A·W-1 was achieved at 1550 nm with a source-drain bias of 1 V. The rise time is 4.8 ms, and the fall time is 6.8 ms. Under light illumination and external bias, the Schottky barrier between the BP and metal was reduced, leading to efficient photocurrent extraction. The unprecedented performance of the BP photodetector indicates intriguing potential for sensing, imaging, and optical communication.