Satellite-ground quantum communication requires single-photon detectors of 850-nm wavelength with both high detection efficiency and large sensitive area. We developed superconducting nanowire single-photon detectors (SNSPDs) on one-dimensional photonic crystals, which acted as optical cavities to enhance the optical absorption, with a sensitive-area diameter of 50 um. The fabricated multimode fiber coupled NbN SNSPDs exhibited a maximum system detection efficiency (DE) of up to 82% and a DE of 78% at a dark count rate of 100 Hz at 850-nm wavelength as well as a system jitter of 105 ps.