In this Letter , the radial velocity variability of the chemically peculiar star \epsilon Ursae Majoris ( \epsilon UMa ) from the sharp cores of the hydrogen lines is investigated . This study is based on the ELODIE archival data obtained at different phases of the rotational cycle . The star exhibits low-amplitude radial velocity variations with a period of P = 5.0887 d. The best Keplerian solution yields an eccentricity e = 0.503 and a minimum mass \sim 14.7 M _ { Jup } on the hypothesis that the rotational axis of \epsilon UMa is perpendicular to the orbital plane . This result indicate that the companion is the brown-dwarf with the projected semi-amplitude variation of the radial velocity K _ { 2 } = 135.9 km { s } ^ { -1 } and the sine of inclination times semi-major axis a _ { 2 } \sin ( i ) = 0.055 au .