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In this paper, we report the discovery of a binary composed of a brown dwarf (BD) and a low-mass M dwarf from observation of the microlensing event OGLE-2014-BLG-0257. The resolution of the very brief caustic crossing combined with the detection of subtle continuous deviation in the lensing light curve induced by the Earth’s orbital motion enable us to precisely measure both the Einstein radius theta(E) and the lens parallax pi(E), which are the two quantities needed to unambiguously determine the mass and distance to the lens. It is found that the companion is a substellar BD with a mass of 0.036 +/- 0.005 M-circle dot (37.7 +/- 5.2 M-J) and it is orbiting an M dwarf with a mass of 0.19 +/- 0.02 M-circle dot. The binary is located at a distance of 1.25 +/- 0.13 kpc toward the Galactic bulge and the projected separation between the binary components is 0.61 +/- 0.07 au. The separation scaled by the mass of the host is 3.2 au/M-circle dot. Based on the assumption that separations scale with masses, the discovered BD is located in the BD desert. With the growing sample of BDs in various environments, microlensing will provide a powerful probe of BDs in the Galaxy.