Although near-infrared photons in telecommunication bands are required for long-distance quantum communication, various quantum information tasks have been performed by using visible photons for the past two decades. Recently, such visible photons from diverse media including atomic quantum memories have also been studied. Optical frequency down-conversion from visible to telecommunication bands while keeping the quantum states is thus required for bridging such wavelength gaps. Here we report demonstration of a quantum interface of frequency down-conversion from visible to telecommunication bands by using a nonlinear crystal, which has a potential to work over wide bandwidths, leading to a high-speed interface of frequency conversion. We achieved the conversion of a picosecond visible photon at 780 nm to a 1,522-nm photon, and observed that the conversion process retained entanglement between the down-converted photon and another photon.