Few-layer black phosphorus (BP) has emerged as a promising 2D material for photodetection in the mid-infrared spectral range given its narrow bandgap. However, a comprehensive understanding of BP photodetector’s response in the mid-infrared is still lacking. In this paper, we study the photoresponse of few-layer BP photodetector in the mid-infrared range from 2.5 to 3.7 µm. We identify broadband photoresponse of BP photodetectors in the mid-infrared and observe saturation of the response with optical power. Through frequency and time domain measurements, we have also identified the two dominate mechanisms in our device to be due to the photovoltaic and photogating effects. Our results provide valuable information for optimization of BP mid-infrared photodetectors toward rivaling the current infrared photodetection technology based on compound semiconductors.