BG Gem is an eclipsing binary with a 91.6-day orbital period. The more massive primary component does not seem to show absorption lines in the spectrum, while the less massive secondary is thought to be a K-type star, possibly a supergiant. These results were obtained with optical low-resolution spectroscopy and photometry. The primary was suggested to be a black hole, although with a low confidence. We present a high-resolution optical spectrum of the system along with new BVR-photometry. Analysis of the spectrum shows that the K-type star rotates rapidly at v sin i = 18 km s^{-1} compared to most evolved stars of this temperature range. We also discuss constraints on the secondary's luminosity using spectroscopic criteria and on the entire system parameters using both the spectrum and photometry.