Single wall carbon nanotube (SWCNT)/Si heterojunction photodetectors have the advantages of high photoresponse ability and simple structure, however, their detection wavelength range are usually lower than 1100 nm, which limits their application in the infrared band. We report a SWCNT/Cu/Si photodetector with both a high photoresponse and a detection range up to the infrared band by depositing a Cu nanoparticles (NPs) layer between a SWCNT film and a n-Si substrate. It was found that the Cu NPs produce strong surface plasmon resonance (SPR) under laser irradiation, which breaks through the limitation of Si band gap and greatly improves the photoresponse of the SWCNT/Cu/Si photodetector in the near infrared band. The responsivity (R) of the photodetector in the wavelength range of 1850–1200 nm reached 2.2–14.15 mA/W, which is the highest value in the reported plasmon enhanced n-Si based photodetectors, and about 20,000 times higher than that of a SWCNT/Si photodetector. Its R value for 1550 nm wavelength used in optical communications reached ~ 8.2 mA/W, which is 64% higher than the previously reported values of commonly used photodetectors. We attribute the significant increase to the strong SPR and low Schottky barrier of Cu with n-Si, which facilitates the generation and transfer of the carriers.