We report the development of the multimode fiber-coupled superconducting nanowire single-photon detector with high system detection efficiency at visible wavelength. The detector consists of a 10.5-nm-thick and 150-nm-wide NbN nanowire meander fabricated on a Si substrate with a multilayer dielectric mirror and a quarter wavelength cavity for obtaining high optical absorptance. The meander area was 35 µm in diameter and coupled with the GRIN-lensed multimode optical fiber with a core diameter of 50 µm. The system reached detection efficiency of 70% with dark count rate of 100 Hz at the wavelength of 635 nm, 3 dB roll-off response counting rate of 8.5 Mcps, and timing jitter of 76 ps.